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.util.*;
/**
 * Author:-Milap Shah
 * College:-DA-IICT
 */
public class Q3 {
 
    public static void main(String[] args) {
        InputReader s = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        /*My code starts here.*/
        
        int n = s.nextInt();
        long w = s.nextLong();
        
        int arr[] = s.nextIntArray(n);
        long cap = 0;
        long totalcap = 0;
        int maxi = 0;
        int max = arr[0];
        Node node[] = new Node[n];
        for(int i=0;i<n;i++)
        {
        	cap += (long)(Math.ceil((double)(arr[i])/2));
        	totalcap += (long)arr[i];
        	node[i] = new Node(i,arr[i]);
        	if(max < arr[i])
        	{
        		max = arr[i];
        		maxi = i;
        	}
        }
        
        Arrays.sort(node);
        if(totalcap < w)
        {
        	out.println("-1");
        }
        else if(cap <= w)
        {
        	long ans[] = new long[n];
        	for(int i=n-1;i>=0;i--)
            {
        		node[i].ans = ((long)(Math.ceil((double)(node[i].val)/2)));
            }
        	w -= cap;
        	int i = n-1;
        	while(w > 0)
        	{
        		long val = (node[i].val - node[i].ans);
        		if(val >= w)
        		{
        			node[i].ans += w;
        			break;
        		}
        		else
        		{
        			node[i].ans += val;
        			w -= val;
        		}
        		i--;
        	}
        	
        	for(int j=0;j<n;j++)
        	{
        		int ind = node[j].i;
        		ans[ind] = node[j].ans;
        	}
        	for(int j=0;j<n;j++)
        	{
        		out.print(ans[j]+" ");
        	}
        }
        else
        	out.println("-1");
        /*My code ends here.*/
        out.close();
    }
    static void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
    static int sieve(int n)
    {
    	boolean isPrime[] = new boolean[n+1];
    	for (int i = 2; i <= n; i++) {
            isPrime[i] = true;
        }

        // mark non-primes <= n using Sieve of Eratosthenes
        for (int factor = 2; factor*factor <= n; factor++) {

            // if factor is prime, then mark multiples of factor as nonprime
            // suffices to consider mutiples factor, factor+1, ...,  n/factor
            if (isPrime[factor]) {
                for (int j = factor; factor*j <= n; j++) {
                    isPrime[factor*j] = false;
                }
            }
        }
        
        int count = 0;
        for(int i=2;i<=n;i++)
        {
        	if(isPrime[i])
        		count++;
        }
        
        return count;
    }
    
	static long PowerMod(long a, long b, long m) {
		long tempo;
		if (b == 0)
			tempo = 1;
		else if (b == 1)
			tempo = a;
		else {
			long temp = PowerMod(a, b / 2, m);
			if (b % 2 == 0)
				tempo = (temp * temp) % m;
			else
				tempo = ((temp * temp) % m) * a % m;
		}
		return tempo;
	}
 
 
    
    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);
        }
    }
}
class Node implements Comparable<Node>{

	int i, val;
	long ans;
	public Node(int i,int val)
	{
		this.i = i;
		this.val = val;
	}
	public int compareTo(Node that) {
		if(this.val == that.val)
		return this.i - that.i;
		return this.val - that.val;
		
	}
	
}