Polycarp invited all his friends to the tea party to celebrate the holiday. He has n cups, one for each of his n friends, with volumes a1, a2, ..., an. His teapot stores w milliliters of tea (w ≤ a1 + a2 + ... + an). Polycarp wants to pour tea in cups in such a way that:

  * Every cup will contain tea for at least half of its volume 
  * Every cup will contain integer number of milliliters of tea 
  * All the tea from the teapot will be poured into cups 
  * All friends will be satisfied. 



Friend with cup i won't be satisfied, if there exists such cup j that cup i contains less tea than cup j but ai > aj.

For each cup output how many milliliters of tea should be poured in it. If it's impossible to pour all the tea and satisfy all conditions then output -1.

Input

The first line contains two integer numbers n and w (1 ≤ n ≤ 100, <image>).

The second line contains n numbers a1, a2, ..., an (1 ≤ ai ≤ 100).

Output

Output how many milliliters of tea every cup should contain. If there are multiple answers, print any of them.

If it's impossible to pour all the tea and satisfy all conditions then output -1.

Examples

Input

2 10
8 7


Output

6 4 


Input

4 4
1 1 1 1


Output

1 1 1 1 


Input

3 10
9 8 10


Output

-1

Note

In the third example you should pour to the first cup at least 5 milliliters, to the second one at least 4, to the third one at least 5. It sums up to 14, which is greater than 10 milliliters available.
import java.util.*;
import java.math.*;
import java.io.*;

public class Luck{
	public static InputReader sc;
    public static PrintWriter out;
    public static final int MOD = (int) (1e9 + 7);
    public static void main(String[] args){
    	sc=new InputReader(System.in);	
    	out=new PrintWriter(System.out);
    	int n=sc.nextInt();
    	int w=sc.nextInt();
    	int[] A=new int[n];
    	int[] ans=new  int[n];
    	TreeMap<Integer,HashSet<Integer>> index=new TreeMap<Integer, HashSet<Integer>>();
    	for(int i=0;i<n;i++){
    		A[i]=sc.nextInt();
    		ans[i]=(A[i]+1)/2;
    		w-=ans[i];
    		//out.println(ans[i]);
    		if(index.containsKey(A[i])){
    			HashSet<Integer> set=index.get(A[i]);
    			set.add(i);
    			index.put(A[i], set);
    		}
    		else{
    			HashSet<Integer> set=new HashSet<Integer>();
    			set.add(i);
    			index.put(A[i], set);
    		}
    	}
    	if(w<0){
    		out.println(-1);
    	}
    	else{
    		//out.println("val: "+val+" "+(w+n-1));
    		for(int i:index.descendingKeySet()){
    			int flag=0;
    			for(int j:index.get(i)){
    				if(w==0){
    					flag=1;
    					break;
    				}
    				int min=Math.min(w, A[j]-ans[j]);
    				ans[j]+=min;
    				w-=min;
    			}
    			if(flag==1){
    				break;
    			}
    		}
    		for(int i=0;i<n;i++){
    			out.print(ans[i]+" ");
    		}
    	}
    	
        out.close();
    }
   
    static int gcd(int a,int b){
    	if(b==0){
    		return a;
    	}
    	return gcd(b,a%b);
    	
    }
    static int lcm(int a,int b){
    	int g;
    	if(a<b){
    		g=gcd(b,a);
    	}
    	else{
    		g=gcd(a,b);
    	}
    	return (a*b)/g;
    }
    
    static boolean isPrime(int n){
    	 if (n == 2)
    	        return true;
    	    for (long i = 2; i * i <= n; i++) {
    	        if (n % i == 0)
    	            return false;
    	    }
    	    return true;
    }
    
    static void shuffle(int[] A){
    	for(int i=A.length-1;i>0;i--){
    		int j=(int)(Math.random()*(i+1));
    		int temp=A[j];
    		A[j]=A[i];
    		A[i]=temp;
    	}
    }
    
	public static class Node implements Comparable<Node>{
	    int v;
	    int d;
	    public Node(){
	    	;
	    }
	    public Node (int v, int d) {
	    	this.d = d;
	        this.v = v;
	        
	    }
	    
	    public void print() {
	        out.println(v + " " + d + " ");
	    }
	   
	    public int compareTo(Node n1){
	    	return this.d-n1.d;
	    }
	}

	public static BigInteger pow(BigInteger base, BigInteger exp) {
	    if(exp.equals(new BigInteger(String.valueOf(0)))){
	        return new BigInteger(String.valueOf(1));
	    }    
	    if(exp.equals(new BigInteger(String.valueOf(1))))
	        return base;
	    BigInteger temp=exp.divide(new BigInteger(String.valueOf(2)));
	    BigInteger val = pow(base, temp);
	    BigInteger result = val.multiply(val);
	    result=result.remainder(new BigInteger(String.valueOf(MOD)));
	    BigInteger AND=exp.and(new BigInteger(String.valueOf(1)));
	    if(AND.equals(new BigInteger(String.valueOf(1)))){
	        result = result.multiply(base);
	        result=result.remainder(new BigInteger(String.valueOf(MOD)));
	    }    
	    return result;
	}
	    
	static class InputReader {

	    private InputStream stream;
	    private byte[] buf = new byte[8192];
	    private int curChar, snumChars;
	    private SpaceCharFilter filter;

	    public InputReader(InputStream stream) {
	        this.stream = stream;
	    }

	    public int snext() {
	        if (snumChars == -1)
	            throw new InputMismatchException();
	        if (curChar >= snumChars) {
	            curChar = 0;
	            try {
	                snumChars = stream.read(buf);
	            } catch (IOException e) {
	                throw new InputMismatchException();
	            }
	            if (snumChars <= 0)
	                return -1;
	        }
	        return buf[curChar++];
	    }

	    public int nextInt() {
	        int c = snext();
	        while (isSpaceChar(c))
	            c = snext();
	        int sgn = 1;
	        if (c == '-') {
	            sgn = -1;
	            c = snext();
	        }
	        int res = 0;
	        do {
	            if (c < '0' || c > '9')
	                throw new InputMismatchException();
	            res *= 10;
	            res += c - '0';
	            c = snext();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }

	    public long nextLong() {
	        int c = snext();
	        while (isSpaceChar(c))
	            c = snext();
	        int sgn = 1;
	        if (c == '-') {
	            sgn = -1;
	            c = snext();
	        }
	        long res = 0;
	        do {
	            if (c < '0' || c > '9')
	                throw new InputMismatchException();
	            res *= 10;
	            res += c - '0';
	            c = snext();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }

	    public int[] nextIntArray(int n) {
	        int a[] = new int[n];
	        for (int i = 0; i < n; i++)
	            a[i] = nextInt();
	        return a;
	    }

	    public String readString() {
	        int c = snext();
	        while (isSpaceChar(c))
	            c = snext();
	        StringBuilder res = new StringBuilder();
	        do {
	            res.appendCodePoint(c);
	            c = snext();
	        } while (!isSpaceChar(c));
	        return res.toString();
	    }

	    public boolean isSpaceChar(int c) {
	        if (filter != null)
	            return filter.isSpaceChar(c);
	        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    }

	    public interface SpaceCharFilter {
	        public boolean isSpaceChar(int ch);
	    }
	}

}

