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.io.*;
	    import java.math.*;
	    import java.util.*;
	    import javax.print.attribute.SetOfIntegerSyntax;
	     
	    public class Main {
	    	private static InputStream stream;
	    	private static byte[] buf = new byte[1024];
	    	private static int curChar;
	    	private static int numChars;
	    	private static SpaceCharFilter filter;
	    	private static PrintWriter pw;
	    	private static long count = 0,mod=1000000007;
	    	private static TreeSet<Integer>ts[]=new TreeSet[200000];
	    	private static HashSet hs=new HashSet();
	     

	    	 public static void main(String[] args) {
		        	InputReader(System.in);
		    		pw = new PrintWriter(System.out); 
		            new Thread(null ,new Runnable(){
		               public void run(){
		                   try{
		                       soln();
		                       pw.close();
		                   } catch(Exception e){
		                       e.printStackTrace();
		                   }
		               }
		           },"1",1<<26).start();
		       }
	     
	     
	    	public static long gcd(long x, long y) {
	    		if (x == 0)
	    			return y;
	    		else
	    			return gcd( y % x,x);
	    	}
	    	
	    	 
	    	// To Get Input
	    	// Some Buffer Methods
	     
	    	public static void InputReader(InputStream stream1) {
	    		stream = stream1;
	    	}
	     
	    	private static boolean isWhitespace(int c) {
	    		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    	}
	     
	    	private static boolean isEndOfLine(int c) {
	    		return c == '\n' || c == '\r' || c == -1;
	    	}
	     
	    	private static int read() {
	    		if (numChars == -1)
	    			throw new InputMismatchException();
	    		if (curChar >= numChars) {
	    			curChar = 0;
	    			try {
	    				numChars = stream.read(buf);
	    			} catch (IOException e) {
	    				throw new InputMismatchException();
	    			}
	    			if (numChars <= 0)
	    				return -1;
	    		}
	    		return buf[curChar++];
	    	}
	     
	    	private static int nextInt() {
	    		int c = read();
	    		while (isSpaceChar(c))
	    			c = read();
	    		int sgn = 1;
	    		if (c == '-') {
	    			sgn = -1;
	    			c = read();
	    		}
	    		int res = 0;
	    		do {
	    			if (c < '0' || c > '9')
	    				throw new InputMismatchException();
	    			res *= 10;
	    			res += c - '0';
	    			c = read();
	    		} while (!isSpaceChar(c));
	    		return res * sgn;
	    	}
	     
	    	private static long nextLong() {
	    		int c = read();
	    		while (isSpaceChar(c))
	    			c = read();
	    		int sgn = 1;
	    		if (c == '-') {
	    			sgn = -1;
	    			c = read();
	    		}
	    		long res = 0;
	    		do {
	    			if (c < '0' || c > '9')
	    				throw new InputMismatchException();
	    			res *= 10;
	    			res += c - '0';
	    			c = read();
	    		} while (!isSpaceChar(c));
	    		return res * sgn;
	    	}
	     
	    	private static String nextToken() {
	    		int c = read();
	    		while (isSpaceChar(c))
	    			c = read();
	    		StringBuilder res = new StringBuilder();
	    		do {
	    			res.appendCodePoint(c);
	    			c = read();
	    		} while (!isSpaceChar(c));
	    		return res.toString();
	    	}
	     
	    	private static String nextLine() {
	    		int c = read();
	    		while (isSpaceChar(c))
	    			c = read();
	    		StringBuilder res = new StringBuilder();
	    		do {
	    			res.appendCodePoint(c);
	    			c = read();
	    		} while (!isEndOfLine(c));
	    		return res.toString();
	    	}
	     
	    	private static int[] nextIntArray(int n) {
	    		int[] arr = new int[n];
	    		for (int i = 0; i < n; i++) {
	    			arr[i] = nextInt();
	    		}
	    		return arr;
	    	}
	     
	    	private static int[][] next2dArray(int n, int m) {
	    		int[][] arr = new int[n][m];
	    		for (int i = 0; i < n; i++) {
	    			for (int j = 0; j < m; j++) {
	    				arr[i][j] = nextInt();
	    			}
	    		}
	    		return arr;
	    	}
	    	private static char[][] nextCharArray(int n,int m){
	    		char [][]c=new char[n][m];
	    		for(int i=0;i<n;i++){
	    			String s=nextLine();
	    			for(int j=0;j<s.length();j++){
	    				c[i][j]=s.charAt(j);
	    			}
	    		}
	    		return c;
	    	}
	     
	    	private static long[] nextLongArray(int n) {
	    		long[] arr = new long[n];
	    		for (int i = 0; i < n; i++) {
	    			arr[i] = nextLong();
	    		}
	    		return arr;
	    	}
	     
	    	private static void pArray(int[] arr) {
	    		for (int i = 0; i < arr.length; i++) {
	    			pw.print(arr[i] + " ");
	    		}
	    		pw.println();
	    		return;
	    	}
	     
	    	private static void pArray(long[] arr) {
	    		for (int i = 0; i < arr.length; i++) {
	    			pw.print(arr[i] + " ");
	    		}
	    		pw.println();
	    		return;
	    	}
	     
	    	private static void pArray(boolean[] arr) {
	    		for (int i = 0; i < arr.length; i++) {
	    			pw.print(arr[i] + " ");
	    		}
	    		pw.println();
	    		return;
	    	}
	     
	    	private static boolean isSpaceChar(int c) {
	    		if (filter != null)
	    			return filter.isSpaceChar(c);
	    		return isWhitespace(c);
	    	}
	     
	    	private interface SpaceCharFilter {
	    		public boolean isSpaceChar(int ch);
	    	}
	     
	    	//----------------------------------------My Code------------------------------------------------//
	
 
	    	
	    	private static void soln() {
	    	    
	    	 	int n=nextInt();
	    	 	int w=nextInt();
	    	 	int temp=w;
	    	 	int[] fcap=new int[n];
	    	 	int[] mreq=new int[n];
	    	 	int treq=0;
	    	 	PriorityQueue<Pair> pq=new PriorityQueue<Pair>();
	    	 	for(int i=0;i<n;i++){
	    	 		
	    	 		int t=nextInt();
	    	 		fcap[i]=t;
	    	 		mreq[i]=(int)Math.ceil(t*1.0/2);
	    	 		treq+=mreq[i];
	    	 		pq.add(new Pair(i,t));
	    	 	}
	    	 	if(w>treq){
	    	 		w-=treq;
	    	 		while(w>0){
	    	 			Pair t=pq.poll();
	    	 			//pw.println(t.x+" "+t.y);
	    	 			int ex=t.y-mreq[t.x];
	    	 			if(ex<=w){
	    	 				w-=ex;
	    	 				mreq[t.x]=t.y;
	    	 			}
	    	 			else{
	    	 				
	    	 				mreq[t.x]+=w;
	    	 				w=0;
	    	 			}
	    	 		}
	    	 		for(int i=0;i<n;i++){
	    	 			pw.print(mreq[i]+" ");
	    	 		}
	    	 	}
	    	 	else if(w==treq){
	    	 		for(int i=0;i<n;i++){
	    	 			pw.print(mreq[i]+" ");
	    	 		}
	    	 	}
	    	 	else {
	    	 		pw.println("-1");
	    	 	}
	    	 	//pw.println(treq+" "+w);
	    	 	/*if(w>treq){
	    	 		w-=treq;
	    	 		for(int i=0;i<n;i++){
	    	 			if(fcap[i]-mreq[i]<=w){
	    	 				mreq[i]=fcap[i];
	    	 				w-=fcap[i]-mreq[i];
	    	 			}
	    	 			else{
	    	 				mreq[i]+=w;
	    	 				break;
	    	 			}
	    	 		}
	    	 	}
	    	 	if(temp>=treq){
	    	 		for(int i=0;i<n;i++){
	    	 			pw.print(mreq[i]+" ");
	    	 		}
	    	 	}
	    	 	else pw.println("-1");*/
	    	}
	    		//-----------------------------------------The End--------------------------------------------------------------------------//
	    
	    
	    
	    	
	 }
	    	
	   
	    
		class Pair implements Comparable<Pair>{
		     
			int x;
			int y;
			Pair(int idx,int val){
				this.x=idx;
				this.y=val;
			}
			@Override
			public int compareTo(Pair o) {
				// TODO Auto-generated method stub
			//	Sort in increasing order
					if(y>o.y){
						return -1;
					}
					else if(y==o.y){
						return 0;
					}
					else return 1;
                        /*if((x>=y)&&o.x<o.y){
                              return 1;
                        }
                        else if((x<y)&&o.x>=o.y){
                              return -1;
                        }
                        else if((x<y)&&(o.x<o.y)){
                              long m,n;
                            
                             m=Math.min(2*x,y);
                             n=Math.min(2*o.x,o.y);
                            m-=Math.min(x,y);
                            n-=Math.min(o.x,o.y);
                            if(m>=n){
                                  return -1;
                            }
                            else return 1;
                             
                             
                        }
                        else return 0;
				/*if(idx<o.idx)
					return 1;
				else if(idx>o.idx)
					return -1;
				else{
					if(val<o.val)
						return 1;
					else
						return -1;
		
				}*/
				
			}
		
		}