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.*;
import java.math.BigInteger;

public class Tester
{
	public static long mod=(long)(1e9+7);
	public static long xx,yy,d;
	static int minPrime[];
	static boolean isPrime[];
	
	public static void main(String[] args) throws IOException 
	{
		InputReader s=new InputReader(System.in);
        OutputStream outputStream = System.out;
        PrintWriter out=new PrintWriter(outputStream);
        
        /*long n = s.nextLong();
        String tmp = "";
        tmp = tmp + n;
        
        long dig = tmp.length();
        long mul = exp(10L, dig-1);
        
        if(dig == 1)
        {
        	out.println("1");
        	out.close();
        	return;
        }
        
        if(n % mul == 0)
        {
        	out.println(mul);
        }
        else
        {
        	int f = (int)tmp.charAt(0) - 48;
        	long year = (f+1)*mul;
        	out.println(year-n);
        }*/
        
        /*int n = s.nextInt();
        int k = s.nextInt();
        
        long a[] = new long[n];
        
        for(int i=0; i<n; i++)
        	a[i] = s.nextLong();
        
        long prefix[] = new long[n];
        prefix[0] = a[0];
        
        for(int i=1; i<n; i++)
        	prefix[i] = prefix[i-1] + a[i];
        
        long sum = 0;
        for(int i=0; i<=n-k; i++)
        {
        	if(i == 0)
        	{
        		sum += prefix[k-1];
        	}
        	else
        	{
        		sum += (prefix[i+k-1] - prefix[i-1]);
        	}
        }
        
        double ans = (double)sum/(n-k+1);
        out.println(ans);*/		
        
        int n = s.nextInt();
        int w = s.nextInt();
        
        int a[] = new int[n];
        
        for(int i=0; i<n; i++)
        	a[i] = s.nextInt();
        
        int sum = 0;
        
        for(int i=0; i<n; i++)
        {
        	if(a[i]%2 == 0)
        		sum += (a[i]/2);
        	else
        		sum += ((a[i]/2) + 1);
        }
        		
        if(sum > w)
        {
        	out.println("-1");
        	out.close();
        	return;
        }
        
        w = w - sum;
        
        int ans[] = new int[n];
        
        for(int i=0; i<n; i++)
        	ans[i] = a[i]%2 == 0 ? a[i]/2 : ((a[i]/2)+1);
        
        boolean mark[] = new boolean[n];
        
        while(w > 0)
        {
        	int max = Integer.MIN_VALUE;
        	int ind = -1;
        	
        	for(int i=0; i<n; i++)
        	{
        		if(a[i] > max && mark[i] == false)
        		{
        			max = a[i];
        			ind = i;
        		}
        	}
        	
        	int rem_cap = a[ind] - ans[ind];
        	if(rem_cap > w)
        	{
        		ans[ind] = ans[ind] + w;
        		break;
        	}
        	else
        	{
        		ans[ind] = a[ind];
        		w = w - rem_cap;
        		mark[ind] = true;
        	}
        }
        
        for(int i=0; i<n; i++)
        	out.print(ans[i]+" ");
        
        
        out.close();
	}  
	
	static void modifiedSieve(int n)
	{
		minPrime = new int[n+1];
		
		for(int i=2; i<=Math.sqrt(n); i++)
		{
			if(minPrime[i] == 0)
			{
				for(int j=i*i; j<=n; j=j+i)
				{
					if(minPrime[j] == 0)
						minPrime[j] = i;
				}
			}
		}
		
		for(int i=2; i<=n; i++)
		{
			if(minPrime[i] == 0)
				minPrime[i] = i;
		}
		
	}
	
	static void Sieve(int n)
	{
		isPrime = new boolean[n+1];
		Arrays.fill(isPrime, true);
		
		isPrime[0]=false;
		isPrime[1]=false;
		
		for(int i=2; i<=Math.sqrt(n); i++)
		{
			if(isPrime[i])
			{
				for(int j=i*i; j<=n; j=j+i)
					isPrime[j]=false;
			}
		}
		
	}
	
	static void extendedEuclid(long A, long B)
	{
		if(B == 0) {
	        d = A;
	        xx = 1;
	        yy = 0;
	    }
	    else {
	        extendedEuclid(B, A%B);
	        long temp = xx;
	        xx = yy;
	        yy = temp - (A/B)*yy;
	    }
	}
	
	static long gcd(long a,long b)
	{
		if(b==0)
			return a;
		
		return gcd(b,a%b);
	}
	
	static long modulo(long x,long y,long p)	
	{
		 long res = 1;
		 x = x % p;  
		 
	    while (y > 0)
	    {
	        if (y%2==1)
	            res = (res*x) % p;
	 
	        y = y>>1;
	        x = (x*x) % p;  
	    }
	    return res;
	}
	
	public static int firstOccurence(int a[], int key)
	{
		int low = 0;
		int high = a.length-1;
		
		while(low <= high)
		{
			int mid = low + (high - low)/2;
			
			if(key <= a[mid])
			{
				high = mid - 1;
			}
			else if(key > mid)
			{
				low = mid + 1;
			}
		}
		
		return low;
	}
	
	public static int lastOccurence(int a[], int key)
	{
		int low = 0;
		int high = a.length-1;
		
		while(low <= high)
		{
			int mid = low + (high - low)/2;
			
			if(key >= a[mid])
			{
				low = mid + 1;
			}
			else if(key < a[mid])
			{
				high = mid - 1;
			}
		}
		
		return high;
	}
	
	public static void debug(Object... o)
	{
		System.out.println(Arrays.deepToString(o));
	}
	
	static long exp(long a, long b)
	{
		if(b==0)
			return 1;
		if(b==1)
			return a;
		if(b==2)
			return a*a;

		if(b%2==0)
			return exp(exp(a,b/2),2);
		else
			return a*exp(exp(a,(b-1)/2),2);
	}

	static class Pair implements Comparable<Pair>
	{
		long x,y;
		Pair(long ii, long cc)
		{
			x=ii;
			y=cc;
		}
		
		public int compareTo(Pair o) 
		{
			if(Long.compare(this.x, o.x) != 0)
				return Long.compare(this.x, o.x);
			else
				return Long.compare(this.y, o.y);
		}
		
		public int hashCode() {
			int hu = (int) (x ^ (x >>> 32));
			int hv = (int) (y ^ (y >>> 32));
			return 31 * hu + hv;
		}
 
		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return x == other.x && y == other.y;
		}
		
		public String toString() {
			return "[x=" + x + ", y=" + y + "]";
		}
		
	}

    static final class InputReader{
        private final InputStream stream;
        private final byte[] buf=new byte[1024];
        private int curChar;
        private int Chars;
        public InputReader(InputStream stream){this.stream=stream;}
        private int read()throws IOException{
            if(curChar>=Chars){
                curChar=0;
                Chars=stream.read(buf);
                if(Chars<=0)
                    return -1;
            }
            return buf[curChar++];
        }
        public final int nextInt()throws IOException{return (int)nextLong();}
        public final long nextLong()throws IOException{
            int c=read();
            while(isSpaceChar(c)){
                c=read();
                if(c==-1) throw new IOException();
            }
            boolean negative=false;
            if(c=='-'){
                negative=true;
                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 negative?(-res):(res);
        }
        public final int[] nextIntBrray(int size)throws IOException{
            int[] arr=new int[size];
            for(int i=0;i<size;i++)arr[i]=nextInt();
            return arr;
        }
        public final String nextString()throws IOException{
            int c=read();
            while(isSpaceChar(c))c=read();
            StringBuilder res=new StringBuilder();
            do{
                res.append((char)c);
                c=read();
            }while(!isSpaceChar(c));
            return res.toString();
        }
        public final String nextLine()throws IOException{
            int c=read();
            while(isSpaceChar(c))c=read();
            StringBuilder res=new StringBuilder();
            do{
                res.append((char)c);
                c=read();
            }while(c!='\n' && c!=-1);
            return res.toString();
        }
        private boolean isSpaceChar(int c)
        {
            return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
        }
    }
 
}