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.io.*;
public class Q1 {
	
	static InputReader in=new InputReader(System.in);
	static PrintWriter out=new PrintWriter(System.out);
	static int T=1,N,M;
	static int A[];
 	static int dp[][];
	static ArrayList<Integer> graph[];
	public static void main(String args[])
	{
		//T=in.readInt();
		int i,j;
		while(T-->0)
		{
 			N=in.readInt();
			M=in.readInt();
			A=new int[N];
			in.inputI0(A,N);
			int tp[]=new int[N];
			i=0;
			for(int x:A)
				tp[i++]=x;
			int ans[]=new int[N];
			for(i=0;i<N;i++)
			{
				int temp = (A[i]+1)/2;
				ans[i]=temp;
				M-=temp;
			}
			//out.println(M);
			boolean visited[]=new boolean[N];
			if(M>0)
			{
				int count=N;
				while(count!=0){
					boolean flag=false;
					int max=0;
					for(i=0;i<N;i++)
					{
						if(!flag&&!visited[i])
						{
							max=i;
							flag=true;
						}
						else
						{
							if(!visited[i]&&A[i]>A[max])
								max=i;
						}
					}
					visited[max]=true;
					if(M>=(A[max]-ans[max]))
					{
						M-=A[max]-ans[max];
						ans[max]=A[max];
					}
					else
					{
						
						ans[max]+=M;
						M=0;
					}
					count--;
					if(M==0)
						break;
				}
				if(M>0)
					out.println("-1");
				else{
					for(int x:ans)
						out.print(x+" ");
					out.println();
				}
			}
			else if(M==0)
			{	
				for(int x: ans)
					out.print(x+" ");
				out.println();
			}
			else
				out.println("-1");
		}
		out.flush();
		out.close();
	}
	public static void printI0(int a[],int n)
	{
		for(int i=0;i<n;i++)
		{
			out.println(a[i]);
		}
	}
	public static void printI1(int a[],int n)
	{
		for(int i=1;i<=n;i++)
		{
			out.println(a[i]);
		}
	}	
	public static void printL0(long a[],int n)
	{
		for(int i=0;i<n;i++)
		{
			out.println(a[i]);
		}
	}
	public static void printL1(long a[],int n)
	{
		for(int i=1;i<=n;i++)
		{
			out.println(a[i]);
		}
	}
	public static void initializeGraph(int n)
	{
		graph=new ArrayList[n+1];
		for(int i=0;i<=n;i++)
			graph[i]=new ArrayList<Integer>();
	}
}
class Pair{
	int x,y;
	public Pair(int x,int y)
	{
		this.x=x;
		this.y=y;
	}
}
class InputReader{
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

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

	public int readInt(){
		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;
	}
	public void inputI0(int a[],int n)
	{
		for(int i=0;i<n;i++)
			a[i]=readInt();
	}
	public void inputI1(int a[],int n)
	{
		for(int i=1;i<=n;i++)
			a[i]=readInt();
	}
	public long readLong() {
		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;
  }
	public void inputL0(long a[],int n)
	{
		for(int i=0;i<n;i++)
			a[i]=readLong();
	}
	public void inputL1(long a[],int n)
	{
		for(int i=1;i<=n;i++)
			a[i]=readLong();
	}
	public double readDouble() {
      int c = read();
      while (isSpaceChar(c))
          c = read();
      int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
      }
		double res = 0;
		while (!isSpaceChar(c) && c != '.') {
			if (c == 'e' || c == 'E')
				return res * Math.pow(10, readInt());
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
      }
		if (c == '.') {
			c = read();
			double m = 1;
			while (!isSpaceChar(c)) {
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, readInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				m /= 10;
				res += (c - '0') * m;
				c = read();
          }
      }
		return res * sgn;
  }

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

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

  	  			 		  	   				 	 							