You have a coins of value n and b coins of value 1. You always pay in exact change, so you want to know if there exist such x and y that if you take x (0 ≤ x ≤ a) coins of value n and y (0 ≤ y ≤ b) coins of value 1, then the total value of taken coins will be S.

You have to answer q independent test cases.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 10^4) — the number of test cases. Then q test cases follow.

The only line of the test case contains four integers a, b, n and S (1 ≤ a, b, n, S ≤ 10^9) — the number of coins of value n, the number of coins of value 1, the value n and the required total value.

Output

For the i-th test case print the answer on it — YES (without quotes) if there exist such x and y that if you take x coins of value n and y coins of value 1, then the total value of taken coins will be S, and NO otherwise.

You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).

Example

Input


4
1 2 3 4
1 2 3 6
5 2 6 27
3 3 5 18


Output


YES
NO
NO
YES
// Hash: h6E571BHJIgv+jXRMN8ex4Bs2Tp6pPmp0/7fB0MGmew=

import java.security.*;
import java.nio.file.*;
import java.lang.annotation.*;
import java.util.stream.*;
import java.util.concurrent.atomic.*;
import java.util.function.*;
import java.util.concurrent.*;
import java.util.*;
import java.text.*;
import java.nio.*;
import java.nio.charset.*;
import java.io.*;
import java.lang.reflect.*;
import java.math.*;



// Solution can be found in Submission.testCase(). psvm method can be found in Main.main(String[] args)
// Please note that the code isn't obfuscated; only compressed


public class Solution {
    public static void main(String[] args) throws Exception {
        Main.main(args);
    }
}


class Main{public static void main(String[]args)throws Exception{Class<?extends AbstractSubmission>clss=A_PaymentWithoutCharge.class;new A_PaymentWithoutCharge().runSubmission();}};







@ContestSubmission(ContestType.CODEFORCES)
@CacheVersion(0)
class A_PaymentWithoutCharge extends AbstractSubmission {

	@Override
	public void testCase() {
		int t = sc.nextInt();
		for (int i = 0; i < t; i++) {
			long a = sc.nextInt();
			long b = sc.nextInt();
			long n = sc.nextInt();
			long S = sc.nextInt();
			out.println(b < (S % n) || b < (S - (n*a)) ? "NO" : "YES");
		}
	}



	@Override
	public void init() {
		// Nothing here! Good for initializing look-up tables or cached values

		// Note that there could be multiple Problem instances running on different threads. Writing static variables
		// here (or anywhere else) could lead to race conditions! Use static initialization instead
	}











	// Set to TRUE to override default (which may both be true or false). Setting to FALSE has no effect

	/* DISABLE-CODE-COMPRESSION: TRUE */
	/* GLOBAL-DISABLE-CODE-COMPRESSION: DEFAULT */
	/* JAVA-6-COMPATIBILITY-MODE: DEFAULT */
	/* KEEP-UNUSED-DEPENDENCIES: DEFAULT */





	
};

abstract class AbstractSubmission{public FastScanner sc;public InputStream in;public PrintStream out;public PrintStream debug;public volatile double score=0;public volatile int testCaseCount=-1;public volatile int testCaseIndex;public volatile double progress=0;public void runSubmission(){runSubmission(false);}public void runSubmission(boolean debug){runSubmission(System.in,System.out,debug);}public void runSubmission(InputStream in,PrintStream out){runSubmission(in,out,false);}public void runSubmission(InputStream in,PrintStream out,boolean debug){runSubmission(in,out,debug?System.err:new VoidPrintStream());}public void runSubmission(InputStream in,OutputStream out,OutputStream debug){this.in=in;this.sc=new FastScanner(this.in);this.out=new PrintStream(out);this.debug=debug instanceof VoidOutputStream||debug instanceof VoidPrintStream?new VoidPrintStream():new DebugPrintStream(debug);ContestType type=getType();testCaseCount=type.testCaseCount;init();if(testCaseCount<=0){testCaseCount=sc.nextInt();sc.nextLine();}testCaseIndex=0;for(testCaseIndex=1;testCaseIndex<=testCaseCount;testCaseIndex++){progress=0;this.out.printf(type.caseString,testCaseIndex,testCaseCount);testCase();}}private class DebugPrintStream extends PrintStream{public DebugPrintStream(OutputStream debug){super(debug);}private Object conv(Object obj){if(obj instanceof byte[])return Arrays.toString((byte[])obj);else if(obj instanceof char[])return Arrays.toString((char[])obj);else if(obj instanceof short[])return Arrays.toString((short[])obj);else if(obj instanceof int[])return Arrays.toString((int[])obj);else if(obj instanceof long[])return Arrays.toString((long[])obj);else if(obj instanceof float[])return Arrays.toString((float[])obj);else if(obj instanceof double[])return Arrays.toString((double[])obj);else if(obj instanceof boolean[])return Arrays.toString((int[])obj);else if(obj instanceof Object[])return Arrays.deepToString((Object[])obj);else return obj;}public void print(Object obj){super.print(conv(obj));}public void println(Object obj){super.println(conv(obj));}}public ContestType getType(){return getType(getClass());}public static ContestType getType(Class<?extends AbstractSubmission>clss){return getAnnotation(clss).value();}private static ContestSubmission getAnnotation(Class<?extends AbstractSubmission>clss){if(!clss.isAnnotationPresent(ContestSubmission.class)){throw new RuntimeException("ContestSubmission annotation not present on class "+clss.getCanonicalName()+ "!");}return clss.getAnnotation(ContestSubmission.class);}public abstract void testCase();public abstract void init();};

class Arr extends ArrayUtils{};

class ArrayUtils{public static void sort(int[]arr){shuffle(arr);Arrays.sort(arr);}public static void sort(long[]arr){shuffle(arr);Arrays.sort(arr);}public static void sort(double[]arr){shuffle(arr);Arrays.sort(arr);}public static<T>void sort(T[]arr){Arrays.sort(arr);}public static<T>void sort(T[]arr,Comparator<?super T>comparator){Arrays.sort(arr,comparator);}public static void shuffle(int[]arr){shuffle(arr,ThreadLocalRandom.current());}public static void shuffle(long[]arr){shuffle(arr,ThreadLocalRandom.current());}public static void shuffle(double[]arr){shuffle(arr,ThreadLocalRandom.current());}public static void shuffle(boolean[]arr){shuffle(arr,ThreadLocalRandom.current());}public static<T>void shuffle(T[]arr){shuffle(arr,ThreadLocalRandom.current());}public static void shuffle(int[]arr,Random random){for(int i=0;i<arr.length-1;i++){swap(arr,i,i+random.nextInt(arr.length-i));}}public static void shuffle(long[]arr,Random random){for(int i=0;i<arr.length-1;i++){swap(arr,i,i+random.nextInt(arr.length-i));}}public static void shuffle(double[]arr,Random random){for(int i=0;i<arr.length-1;i++){swap(arr,i,i+random.nextInt(arr.length-i));}}public static<T>void shuffle(T[]arr,Random random){for(int i=0;i<arr.length-1;i++){swap(arr,i,i+random.nextInt(arr.length-i));}}public static void shuffle(boolean[]arr,Random random){for(int i=0;i<arr.length-1;i++){swap(arr,i,i+random.nextInt(arr.length-i));}}public static void swap(int[]arr,int i,int j){int tmp=arr[i];arr[i]=arr[j];arr[j]=tmp;}public static void swap(long[]arr,int i,int j){long tmp=arr[i];arr[i]=arr[j];arr[j]=tmp;}public static void swap(double[]arr,int i,int j){double tmp=arr[i];arr[i]=arr[j];arr[j]=tmp;}public static void swap(boolean[]arr,int i,int j){boolean tmp=arr[i];arr[i]=arr[j];arr[j]=tmp;}public static<T>void swap(T[]arr,int i,int j){T tmp=arr[i];arr[i]=arr[j];arr[j]=tmp;}public static int indexOf(int[]arr,int of){for(int i=0;i<arr.length;i++){if(arr[i]==of)return i;}return-1;}public static int indexOf(boolean[]arr,boolean of){for(int i=0;i<arr.length;i++){if(arr[i]==of)return i;}return-1;}public static int indexOf(double[]arr,double of){for(int i=0;i<arr.length;i++){if(arr[i]==of)return i;}return-1;}public static int indexOf(long[]arr,long of){for(int i=0;i<arr.length;i++){if(arr[i]==of)return i;}return-1;}public static int indexOf(Object[]arr,Object of){for(int i=0;i<arr.length;i++){if(Utils.equals(arr[i],of))return i;}return-1;}public static int[]toIntArray(byte[]arr){return asList(arr).stream().mapToInt(a->a).toArray();}public static int[]toIntArray(short[]arr){return asList(arr).stream().mapToInt(a->a).toArray();}public static int[]toIntArray(char[]arr){return asList(arr).stream().mapToInt(a->a).toArray();}public static long[]toLongArray(byte[]arr){return asList(arr).stream().mapToLong(a->a).toArray();}public static long[]toLongArray(short[]arr){return asList(arr).stream().mapToLong(a->a).toArray();}public static long[]toLongArray(char[]arr){return asList(arr).stream().mapToLong(a->a).toArray();}public static long[]toLongArray(int[]arr){return Arrays.stream(arr).mapToLong(a->a).toArray();}public static double[]toDoubleArray(float[]arr){return asList(arr).stream().mapToDouble(a->a).toArray();}public static List<Byte>asList(byte[]arr){return new BackedList<>(arr);}public static List<Character>asList(char[]arr){return new BackedList<>(arr);}public static List<Short>asList(short[]arr){return new BackedList<>(arr);}public static List<Integer>asList(int[]arr){return new BackedList<>(arr);}public static List<Boolean>asList(boolean[]arr){return new BackedList<>(arr);}public static List<Float>asList(float[]arr){return new BackedList<>(arr);}public static List<Double>asList(double[]arr){return new BackedList<>(arr);}public static List<Long>asList(long[]arr){return new BackedList<>(arr);}public static<T>List<T>asList(T[]arr){return Arrays.asList(arr);}private static class BackedList<T,A>extends AbstractList<T>{private A arr;private int length;public BackedList(A arr){this.arr=arr;this.length=java.lang.reflect.Array.getLength(arr);}public T get(int index){return(T)java.lang.reflect.Array.get(arr,index);}public T set(int index,T val){T oldValue=get(index);java.lang.reflect.Array.set(arr,index,val);return oldValue;}public int size(){return length;}}public static<T>Iterator<T>iterator(T...arr){return asList(arr).iterator();}public static int verboseCopy(byte[]src,int srcFromIndex,int srcToIndex,byte[]dest,int destFromIndex){int length=srcToIndex-srcFromIndex;if(length<0){length+=src.length;int copied=verboseCopy(src,srcFromIndex,src.length,dest,destFromIndex);return copied+verboseCopy(src,0,srcToIndex,dest,destFromIndex+copied);}else{System.arraycopy(src,srcFromIndex,dest,destFromIndex,length);return length;}}public static int verboseCopy(int[]src,int srcFromIndex,int srcToIndex,int[]dest,int destFromIndex){int length=srcToIndex-srcFromIndex;if(length<0){length+=src.length;int copied=verboseCopy(src,srcFromIndex,src.length,dest,destFromIndex);return copied+verboseCopy(src,0,srcToIndex,dest,destFromIndex+copied);}else{System.arraycopy(src,srcFromIndex,dest,destFromIndex,length);return length;}}public static int verboseCopy(long[]src,int srcFromIndex,int srcToIndex,long[]dest,int destFromIndex){int length=srcToIndex-srcFromIndex;if(length<0){length+=src.length;int copied=verboseCopy(src,srcFromIndex,src.length,dest,destFromIndex);return copied+verboseCopy(src,0,srcToIndex,dest,destFromIndex+copied);}else{System.arraycopy(src,srcFromIndex,dest,destFromIndex,length);return length;}}public static int verboseCopy(double[]src,int srcFromIndex,int srcToIndex,double[]dest,int destFromIndex){int length=srcToIndex-srcFromIndex;if(length<0){length+=src.length;int copied=verboseCopy(src,srcFromIndex,src.length,dest,destFromIndex);return copied+verboseCopy(src,0,srcToIndex,dest,destFromIndex+copied);}else{System.arraycopy(src,srcFromIndex,dest,destFromIndex,length);return length;}}public static<T>int verboseCopy(T[]src,int srcFromIndex,int srcToIndex,T[]dest,int destFromIndex){int length=srcToIndex-srcFromIndex;if(length<0){length+=src.length;int copied=verboseCopy(src,srcFromIndex,src.length,dest,destFromIndex);return copied+verboseCopy(src,0,srcToIndex,dest,destFromIndex+copied);}else{System.arraycopy(src,srcFromIndex,dest,destFromIndex,length);return length;}}};

@Retention(RetentionPolicy.RUNTIME)@Target(ElementType.TYPE)@interface CacheVersion{int value();};

@Retention(RetentionPolicy.RUNTIME)@Target(ElementType.TYPE)@interface ContestSubmission{ContestType value();};

enum ContestType{PLAIN("",-1),ETH_JUDGE("",-1,null,false,false,6),GOOGLE("Case #%d: ",-1),GOOGLE_JAM("Case #%d: ",-1, "Solution.java",false,false,8),GOOGLE_JAM_INTERACTIVE("",-1, "Solution.java",false,false,8),FACEBOOK("Case #%d: ",-1),BLOOMBERG("",1, "Problem.java",false,false,8),SINGLE_TESTCASE("",1),OPTIMIZER("",1,null,false,false,8,true),HACKERRANK("",1, "Solution.java",false,false,8),CODEFORCES("",1, "Solution.java",false,false,8);public int testCaseCount;public String caseString;public String launcher;public boolean disableCompression;public boolean keepUnusedDependencies;public int javaVersion;public boolean isOptimizer;ContestType(String caseString,int testCaseCount,String launcher,boolean disableCompression,boolean keepUnusedDependencies,int javaVersion,boolean isOptimizer){this.caseString=caseString;this.testCaseCount=testCaseCount;this.launcher=launcher;this.disableCompression=disableCompression;this.javaVersion=javaVersion;this.keepUnusedDependencies=keepUnusedDependencies;this.isOptimizer=isOptimizer;}ContestType(String a1,int a2,String a3,boolean a4,boolean a5,int a6){this(a1,a2,a3,a4,a5,a6,false);}ContestType(String a1,int a2){this(a1,a2,null,false,false,8);}};

class FastScanner{private static String spaceDelimiters= " \t\n\r\f";private BufferedReader buffer;private StringTokenizer tokenizer;private InputStream stream;public FastScanner(InputStream stream){this.stream=stream;}public String nextLine(){if(this.buffer==null)this.buffer=new BufferedReader(new InputStreamReader(stream));while(tokenizer==null){try{tokenizer=new StringTokenizer(buffer.readLine()+ "\n");}catch(IOException e){throw new RuntimeException("IO exception occured!",e);}}String res=tokenizer.nextToken("");if(!res.endsWith("\n"))throw new RuntimeException("waddaheq just heppenenened");res=res.substring(0,res.length()-1);if(res.contains("\n"))throw new RuntimeException("oke wat lamo");tokenizer=null;return res;}public String next(){if(this.buffer==null)this.buffer=new BufferedReader(new InputStreamReader(stream));while(tokenizer==null||!tokenizer.hasMoreTokens()){try{tokenizer=new StringTokenizer(buffer.readLine()+ "\n");}catch(IOException e){throw new RuntimeException("IO exception occured!",e);}}return tokenizer.nextToken(spaceDelimiters);}public BigDecimal nextBigDecimal(){return new BigDecimal(next());}public BigInteger nextBigInteger(){return new BigInteger(next());}public int nextInt(){return Integer.parseInt(next());}public long nextLong(){return Long.parseLong(next());}public double nextDouble(){return Double.parseDouble(next());}};

@Retention(RetentionPolicy.SOURCE)@Target(ElementType.METHOD)@interface O{String value();};

@Target(ElementType.FIELD)@Retention(RetentionPolicy.RUNTIME)@interface Optimize{long imin()default 0;long imax()default 100;double fmin()default 0;double fmax()default 1;};

class Utils{public static boolean equals(int a,int b){return a==b;}public static boolean equals(long a,long b){return a==b;}public static boolean equals(double a,double b){return Double.doubleToLongBits(a)==Double.doubleToLongBits(b);}public static boolean equals(Object a,Object b){return Objects.equals(a,b);}public static int hashCode(int a){return Integer.hashCode(a);}public static int hashCode(long a){return Long.hashCode(a);}public static int hashCode(double a){return Double.hashCode(a);}public static int hashCode(Object a){return Objects.hashCode(a);}public static int compare(int a,int b){return Integer.compare(a,b);}public static int compare(long a,long b){return Long.compare(a,b);}public static int compare(double a,double b){return Double.compare(a,b);}public static<T extends Comparable<?super T>>int compare(T a,T b){return Objects.compare(a,b,Comparator.naturalOrder());}public static<T>int hashAll(Object...objs){return hashAll(Arr.iterator(objs));}public static<T>int hashAll(Iterator<T>iterator){int hash=1;while(iterator.hasNext()){T obj=iterator.next();hash=hash*31+Objects.hashCode(obj);}return hash;}public static void repeat(int times,Consumer<Integer>consumer){for(int i=0;i<times;i++){consumer.accept(i);}}public static void repeat(int times,Runnable runnable){repeat(times,(a)->runnable.run());}public static<E extends Throwable>double timing(ThrowingRunnable<E>runnable)throws E{long start=System.nanoTime();runnable.run();long end=System.nanoTime();return(end-start)/1_000_000_000.0;}private static int timingId=0;public static<T,E extends Throwable>T printTiming(ThrowingSupplier<T,E>supplier,String name)throws E{int tid=timingId++;if(name==null)name= ""+tid;else name=tid+ " - "+name;System.err.println("Starting task "+name);long start=System.nanoTime();try{return supplier.get();}finally{long end=System.nanoTime();System.err.println("Time taken for task "+name+ ": "+(end-start)/1_000_000_000.0+ "s");}}public static<E extends Throwable>void printTiming(ThrowingRunnable<E>runnable,String name)throws E{printTiming(()->{runnable.run();return null;},name);}public static<E extends Throwable>void printTiming(ThrowingRunnable<E>runnable)throws E{printTiming(runnable,null);}public static<T,E extends Throwable>T printTiming(ThrowingSupplier<T,E>supplier)throws E{return printTiming(supplier,null);}public static<T>ArrayList<T>toArrayList(Iterable<T>iterable){int size=iterable instanceof Collection?((Collection)iterable).size():-1;return toArrayList(iterable,size);}public static<T>ArrayList<T>toArrayList(Iterable<T>iterable,int size){return toArrayList(iterable.iterator(),size);}public static<T>ArrayList<T>toArrayList(Iterator<T>iterator){return toArrayList(iterator,-1);}public static<T>ArrayList<T>toArrayList(Iterator<T>iterator,int estimatedSize){return toArrayList(Spliterators.spliterator(iterator,estimatedSize,Spliterator.ORDERED));}public static<T>ArrayList<T>toArrayList(Spliterator<T>spliterator){long estimatedSize=spliterator.estimateSize();if(estimatedSize>=Long.MAX_VALUE||estimatedSize<=10)estimatedSize=10;ArrayList<T>result=new ArrayList<>((int)Math.min(estimatedSize,Integer.MAX_VALUE));spliterator.forEachRemaining(result::add);return result;}public static PrimitiveIterator.OfInt toPrimitiveIterator(IntIterator iterator){return new PrimitiveIterator.OfInt(){public int nextInt(){return iterator.next();}public boolean hasNext(){return iterator.hasNext();}};}public static PrimitiveIterator.OfLong toPrimitiveIterator(LongIterator iterator){return new PrimitiveIterator.OfLong(){public long nextLong(){return iterator.next();}public boolean hasNext(){return iterator.hasNext();}};}public static PrimitiveIterator.OfDouble toPrimitiveIterator(DoubleIterator iterator){return new PrimitiveIterator.OfDouble(){public double nextDouble(){return iterator.next();}public boolean hasNext(){return iterator.hasNext();}};}public static IntStream stream(IntIterator iterator){return stream(iterator,-1);}public static IntStream stream(IntIterator iterator,int estimatedSize){return stream(Spliterators.spliterator(Utils.toPrimitiveIterator(iterator),estimatedSize,Spliterator.ORDERED));}public static IntStream stream(Spliterator.OfInt spliterator){return StreamSupport.intStream(spliterator,false);}public static LongStream stream(LongIterator iterator){return stream(iterator,-1);}public static LongStream stream(LongIterator iterator,int estimatedSize){return stream(Spliterators.spliterator(Utils.toPrimitiveIterator(iterator),estimatedSize,Spliterator.ORDERED));}public static LongStream stream(Spliterator.OfLong spliterator){return StreamSupport.longStream(spliterator,false);}public static DoubleStream stream(DoubleIterator iterator){return stream(iterator,-1);}public static DoubleStream stream(DoubleIterator iterator,int estimatedSize){return stream(Spliterators.spliterator(Utils.toPrimitiveIterator(iterator),estimatedSize,Spliterator.ORDERED));}public static DoubleStream stream(Spliterator.OfDouble spliterator){return StreamSupport.doubleStream(spliterator,false);}public static<T>Stream<T>stream(Iterator<T>iterator){return stream(iterator,-1);}public static<T>Stream<T>stream(Iterator<T>iterator,int estimatedSize){return stream(Spliterators.spliterator(iterator,estimatedSize,Spliterator.ORDERED));}public static<T>Stream<T>stream(Spliterator<T>spliterator){return StreamSupport.stream(spliterator,false);}public static<T>Map<T,Set<Integer>>invert(Collection<T>coll){Map<T,Set<Integer>>map=new HashMap<>();int i=0;for(T t:coll){Set<Integer>set=map.get(t);if(set==null){map.put(t,Collections.singleton(i));}else{if(!(set instanceof LinkedHashSet)){set=new LinkedHashSet<>(set);map.put(t,set);}set.add(i);}i++;}return Collections.unmodifiableMap(map);}public static<T>ArrayList<T>arrayListOfSize(int size){return arrayListOfSize(size,null);}public static<T>ArrayList<T>arrayListOfSize(int size,T element){return new ArrayList<>(Collections.nCopies(size,element));}public static<T>Set<T>asSet(Collection<T>uniqueElements){return asModifiableSet(Collections.unmodifiableCollection(uniqueElements));}public static<T>Set<T>asModifiableSet(Collection<T>uniqueElements){return new AbstractSet<T>(){public int size(){return uniqueElements.size();}public boolean isEmpty(){return uniqueElements.isEmpty();}public boolean contains(Object o){return uniqueElements.contains(o);}public Iterator<T>iterator(){return uniqueElements.iterator();}public Object[]toArray(){return uniqueElements.toArray();}public<T1>T1[]toArray(T1[]a){return uniqueElements.toArray(a);}public boolean add(T t){return uniqueElements.add(t);}public boolean remove(Object o){return uniqueElements.remove(o);}public boolean containsAll(Collection<?>c){return uniqueElements.containsAll(c);}public boolean addAll(Collection<?extends T>c){return uniqueElements.addAll(c);}public boolean retainAll(Collection<?>c){return uniqueElements.retainAll(c);}public boolean removeAll(Collection<?>c){return uniqueElements.removeAll(c);}public void clear(){uniqueElements.clear();}};}public static<T>Collector<T,?,Set<T>>collectToSet(){return Collectors.collectingAndThen(Collectors.toList(),Utils::asSet);}public static<T>ListIterator<T>reverseIterator(List<T>list){return reverseIterator(list.listIterator(list.size()));}public static<T>ListIterator<T>reverseIterator(ListIterator<T>it){return new ListIterator<T>(){public boolean hasNext(){return it.hasPrevious();}public T next(){return it.previous();}public boolean hasPrevious(){return it.hasNext();}public T previous(){return it.next();}public int nextIndex(){return it.previousIndex();}public int previousIndex(){return it.nextIndex();}public void remove(){it.remove();}public void set(T t){it.set(t);}public void add(T t){it.add(t);}};}public static<T>Iterable<T>reverseIterable(List<T>list){return()->reverseIterator(list);}public static Runnable nonThrowing(ThrowingRunnable<?>r){return()->{try{r.run();}catch(Throwable e){throw new RuntimeException(e);}};}public static<T>Supplier<T>nonThrowing(ThrowingSupplier<T,?>r){return()->{try{return r.get();}catch(Throwable e){throw new RuntimeException(e);}};}public static<T,R>Function<T,R>nonThrowing(ThrowingFunction<T,R,?>r){return(a)->{try{return r.apply(a);}catch(Throwable e){throw new RuntimeException(e);}};}public static<T>Predicate<T>nonThrowingPredicate(ThrowingPredicate<T,?>r){return(a)->{try{return r.test(a);}catch(Throwable e){throw new RuntimeException(e);}};}private static Map<Class,Class>primitiveClassWrappers=new HashMap<Class,Class>(){{put(boolean.class,Boolean.class);put(byte.class,Byte.class);put(short.class,Short.class);put(char.class,Character.class);put(int.class,Integer.class);put(long.class,Long.class);put(float.class,Float.class);put(double.class,Double.class);}};public static Class<?>primitiveToWrapper(Class<?>clss){return primitiveClassWrappers.getOrDefault(clss,clss);}};

interface DoubleIterator{double next();boolean hasNext();default void forEachRemaining(DoubleConsumer consumer){while(hasNext()){consumer.accept(next());}}};

interface IntIterator{int next();boolean hasNext();default void forEachRemaining(IntConsumer consumer){while(hasNext()){consumer.accept(next());}}};

interface LongIterator{long next();boolean hasNext();default void forEachRemaining(LongConsumer consumer){while(hasNext()){consumer.accept(next());}}};

@FunctionalInterface interface ThrowingFunction<T,R,E extends Throwable>{R apply(T t)throws E;};

@FunctionalInterface interface ThrowingPredicate<T,E extends Throwable>{boolean test(T t)throws E;};

@FunctionalInterface interface ThrowingRunnable<E extends Throwable>{void run()throws E;};

@FunctionalInterface interface ThrowingSupplier<T,E extends Throwable>{T get()throws E;};

class VoidOutputStream extends OutputStream{public void write(int b){return;}public void write(byte b[]){return;}public void write(byte b[],int off,int len){return;}};

class VoidPrintStream extends PrintStream{public VoidPrintStream(){super(new VoidOutputStream());}public void write(int b){return;}public void print(char[]buf){return;}public void print(String s){return;}public void print(Object obj){return;}public void println(char[]buf){return;}public void println(String s){return;}public void println(Object obj){return;}public PrintStream format(Locale l,String s,Object...objs){return this;}public PrintStream format(String s,Object...objs){return this;}};