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.*;
import java.math.*;
import java.lang.*;
import static java.lang.Math.*;
 
public class Sol
{
    
    static long mod=1000000007;
    
    public static void main(String args[]) throws Exception
    {
        InputReader in;
        PrintWriter w;
        boolean online = false;
        String fileName = "input";

        if (online) 
        {
            in = new InputReader(new FileInputStream(new File(fileName + ".in")));
            w = new PrintWriter(new FileWriter("out.txt"));
        } 
        else 
        {
            in = new InputReader(System.in);
            w = new PrintWriter(System.out);
        }
        
        //int T = in.nextInt();
        int T=1;
        
        for (int t = 1; t <= T; t++) 
        {
            int n=in.nextInt();
            int tea=in.nextInt();
            
            int a[]=new int[n];
            
            Integer b[][]=new Integer[n][2];
            int mintot=0;
            
            for(int i=0;i<n;i++)
            {
                a[i]=in.nextInt();
                b[i][0]=a[i];
                
                int x=a[i]/2;
                
                if(a[i]%2!=0)
                    x++;
                
                mintot+=x;
                
                b[i][1]=x;
            }
            
            Arrays.sort(b, new Comparator<Integer[]>() 
            {
                public int compare(Integer[] int1, Integer[] int2) 
                {
                    Integer numOfKeys1 = int1[0];       //about which column u want to sort
                    Integer numOfKeys2 = int2[0];
                    return numOfKeys1.compareTo(numOfKeys2);
                }
            });
            
            
            if(mintot>tea)
                w.println("-1");
            
            else
            {
                tea-=mintot;
                int ind=n-1;
                
                if(tea!=0)
                {
                    while(true)
                    {
                        int done=b[ind][1];
                        int limit=b[ind][0];
                        
                        limit-=done;
                        
                        if(limit<tea)
                        {
                            b[ind][1]=b[ind][0];
                            tea-=limit;
                            ind--;
                        }
                        
                        else
                        {
                            done+=tea;
                            b[ind][1]=done;
                            break;
                        }
                    }
                }
                
                for(int i=0;i<n;i++)
                {
                    for(int j=0;j<n;j++)
                    {
                        if(a[i]==b[j][0])
                        {
                            if(b[j][1]!=-1)
                            {
                                w.print(b[j][1]+" ");
                                b[j][1]=-1;
                                break;
                            }
                        }
                    }
                }
            }
        }
        
        w.close();
    }
    
    static int arr[];
    static int size[];
    
    static void initialize(int n)
    {
        for(int i=0;i<=n;i++)
        {
            arr[i]=i;
            size[i]=1;
        }
    }
    
    static int root(int r)
    {
        while(arr[r]!=r)
        {
            arr[r]=arr[arr[r]];
            r=arr[r];
        }
        
        return r;
    }
    
    static void union(int u,int v)
    {
        int r1=root(u);
        int r2=root(v);

        if(r1!=r2)
        {
            if(size[r1]<size[r2])
            {
                arr[r1]=arr[r2];
                size[r2]+=size[r1];
            }

            else
            {
                arr[r2]=arr[r1];
                size[r1]+=size[r2];
            }
        }
    }
    
    private static long gcd(long a, long b)
    {
        while (b > 0)
        {
            long temp = b;
            b = a % b; // % is remainder
            a = temp;
        }
        return a;
    }
 
    private static long gcd(long[] input)
    {
        long result = input[0];
        
        for(int i = 1; i < input.length; i++) 
            result = gcd(result, input[i]);
        
        return result;
    }
    
    private static long lcm(long a, long b)
    {
        return a * (b / gcd(a, b));
    }
 
    private static long lcm(long[] input)
    {
        long result = input[0];
        
        for(int i = 1; i < input.length; i++) 
            result = lcm(result, input[i]);
        
        return result;
    }
    
    public static void Array_2dsort(Integer[][] a)
    {
        Arrays.sort(a, new Comparator<Integer[]>() 
        {
            public int compare(Integer[] int1, Integer[] int2) 
            {
                Integer numOfKeys1 = int1[1];       //about which column u want to sort
                Integer numOfKeys2 = int2[1];
                return numOfKeys1.compareTo(numOfKeys2);
            }
        });
    }
     
    static long powmod(long x,long n,long m)        //(a/b)%mod = (a * (b^(m-2))%mod  here --> x=a, n=mod-2, m=mod  
    {
	if (n == 0)
            return 1;
        else if (n%2==0)
            return powmod(((x%m)*(x%m))%m,n/2,m);
	else if(n%2==1)
            return (((x%m)*powmod(((x%m)*(x%m))%m,(n-1)/2,m))%m);
	else
            return 0;
    }
        
	
	static 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 String nextLine()
		{
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
		}
		public 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;
		}
		
		public 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;
		}
		
		public double nextDouble() 
		{
			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, nextInt());
				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, nextInt());
					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);
		}
	}
    
}