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.lang.*;
import java.io.*;

// SHIVAM GUPTA :
//NSIT
//decoder_1671
//BEING PERFECTIONIST IS NOT AN OPTION



// ASCII = 48 + i ;

// SHIVAM GUPTA :


/* Name of the class has to be "Main" only if the class is public. */



public class Main
{
     
     
     
    static PrintWriter out;
    
	static class FastReader{
		BufferedReader br;
		StringTokenizer st;
		public FastReader(){
			br=new BufferedReader(new InputStreamReader(System.in));
			out=new PrintWriter(System.out);
		}
		String next(){
			while(st==null || !st.hasMoreElements()){
				try{
					st= new StringTokenizer(br.readLine());
				}
				catch (IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		int nextInt(){
			return Integer.parseInt(next());
		}
		long nextLong(){
			return Long.parseLong(next());
		}
		double nextDouble(){
			return Double.parseDouble(next());
		}
		String nextLine(){
			String str = "";
			try{
				str=br.readLine();
			}
			catch(IOException e){
				e.printStackTrace();
			}
			return str;
		}
	}
	





/////////////////////////////////////////////////////////////////////////////////////

public static int  min(int a ,int b , int c, int d)
{
       
       
       int[] arr = new int[4] ;
       arr[0] = a;
       arr[1] = b ;
       arr[2] = c;
       arr[3] = d;
       Arrays.sort(arr) ;
       
       return arr[0];
       
}
 
 /////////////////////////////////////////////////////////////////////////////
 
 
public static int  max(int a ,int b , int c, int d)
{
       
       
       int[] arr = new int[4] ;
       arr[0] = a;
       arr[1] = b ;
       arr[2] = c;
       arr[3] = d;
       Arrays.sort(arr) ;
       
       return arr[3];
       
}
 
/////////////////////////////////////////////////////////////////////////////////// 
static int sieve =  1000000 ;

 
static boolean[] prime =  new boolean[sieve + 1] ;

static int[] dp =  new int[10000001] ;

 
public static void sieveOfEratosthenes() 
    { 
        // FALSE == prime
        
        // TRUE ==  COMPOSITE
        
        // FALSE== 1
       
        for(int i=0;i< sieve + 1;i++) 
            prime[i] = false; 
          
        for(int p = 2; p*p <= sieve; p++) 
        { 
           
            if(prime[p] == false) 
            { 
                
                for(int i = p*p; i <= sieve; i += p) 
                    prime[i] = true; 
            } 
        } 
          
       
       
    
    } 
 
///////////////////////////////////////////////////////////////////////////////////


public static String reverse(String input)
{
    String op = "" ;
    
    for(int i = 0; i < input.length() ; i++ )
    {
        op = input.charAt(i)+  op ; 
    }
    
return op ;
}


///////////////////////////////////////////////////////////////////////////////////////


public static void sortD(int[] arr)
{
      sort(arr ,0 , arr.length-1) ;
      
      int i =0 ; int j = arr.length -1  ;
      
      while( i < j)
      {
            int temp = arr[i] ;
            arr[i] =arr[j] ;
            arr[j] = temp ;
            i++ ; j-- ;
      }
      
      
      
      return ;
}

///////////////////////////////////////////////////////////////////////////////////////

public static boolean sameParity(long a  ,long b )
{
      
      if(a%2 == b %2)
      {
            return true  ;
      }
      else{
            return false  ;
      }
}


///////////////////////////////////////////////////////////////////////////////////////

public static boolean sameParity(int a  ,int b )
{
      
      if(a%2 == b %2)
      {
            return true  ;
      }
      else{
            return false  ;
      }
}

////////////////////////////////////////////////////////////////////////////////////

public static boolean isPossibleTriangle(int a  ,int b , int c)
{
      if( a + b > c && c+b > a && a +c > b)
      {
            return true  ;
      }
      
      return false  ;
      
      
}

/////////////////////////////////////////////////////////////////////
    
public static int gcd(int a, int b )
{

if(b==0)return a ;

else return gcd(b,a%b) ; 


}

////////////////////////////////////////////////////////////////////////////////////

public static int lcm(int a, int b ,int c , int d )
{

int temp = lcm(a,b , c) ;


 
 int ans = lcm(temp ,d ) ;

return ans  ;


}

//////////////////////////////////////////////////////////////////////////////////////

public static int lcm(int a, int b ,int c )
{

int temp = lcm(a,b) ;

int ans =  lcm(temp ,c) ;

return ans  ;


}

////////////////////////////////////////////////////////////////////////////////////////
    
public static int lcm(int a , int b )
{

int gc = gcd(a,b);

return (a*b)/gc ;




}

/////////////////////////////////////////////////////////////////////////////////////////////

static boolean isPrime(int n)
{
      if(n==1)
      {
            return false  ;
      }
      
      boolean ans =  true  ;
      
      for(int i = 2; i*i <= n ;i++)
      {
            if(n% i ==0)
            {
                  ans = false  ;break ;
            }
      }
      
      
      return ans  ;
      
      
}
//////////////////////////////////////////////////////////////////////////////////////////
public static long nCr(int n,int k)
{
    long ans=1;
    k=k>n-k?n-k:k;
    int j=1;
    for(;j<=k;j++,n--)
    {
        if(n%j==0)
        {
            ans*=n/j;
        }else
        if(ans%j==0)
        {
            ans=ans/j*n;
        }else
        {
            ans=(ans*n)/j;
        }
    }
    return ans;
}
///////////////////////////////////////////////////////////////////////////////////////////

public static ArrayList<Integer> allFactors(int n)
{   
      ArrayList<Integer> list = new ArrayList<>() ;
      
    for(int i = 1; i*i <= n ;i++)
    {
          if( n % i == 0)
          {
              if(i*i == n)
              {
                    list.add(i) ;
              }
              else{
                    list.add(i) ;
                    list.add(n/i) ;
                    
              }
          }
    }
      
     return list ; 
      
      
}



/////////////////////////////////////////////////////////////////////////////

public static boolean isPowerOfTwo(int n) 
{ 
    if(n==0) 
    return false; 
  
if(((n ) & (n-1)) == 0 ) return true ;
else return false  ;

} 
   
////////////////////////////////////////////////////////////////////////////////////   
   
    public static int countDigit(long n) 
    { 
        return (int)Math.floor(Math.log10(n) + 1); 
    } 
    
 ///////////////////////////////////////////////////////////////////////////////////////// 
  
   static final int MAXN = 100001; 
       
    
    static int spf[] = new int[MAXN]; 
   
    static void sieve() 
    { 
        spf[1] = 1; 
        for (int i=2; i<MAXN; i++) 
       
           
            spf[i] = i; 
       
       
        for (int i=4; i<MAXN; i+=2) 
            spf[i] = 2; 
       
        for (int i=3; i*i<MAXN; i++) 
        { 
           
            if (spf[i] == i) 
            { 
               
                for (int j=i*i; j<MAXN; j+=i) 
       
                    if (spf[j]==j) 
                        spf[j] = i; 
            } 
        } 
    } 
       
// The above code works well for n upto the order of 10^7.
// Beyond this we will face memory issues.

// Time Complexity: The precomputation for smallest prime factor is done in O(n log log n)
// using sieve.
// Where as in the calculation step we are dividing the number every time by 
// the smallest prime number till it becomes 1.
// So, let’s consider a worst case in which every time the SPF is 2 .
// Therefore will have log n division steps.


// Hence, We can say that our Time Complexity will be O(log n) in worst case.


    static Vector<Integer> getFactorization(int x) 
    { 
        Vector<Integer> ret = new Vector<>(); 
        while (x != 1) 
        { 
            ret.add(spf[x]); 
            x = x / spf[x]; 
        } 
        return ret; 
    } 
       
  
   
public static void merge(int arr[], int l, int m, int r)
    {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;
 
        /* Create temp arrays */
        int L[] = new int [n1];
        int R[] = new int [n2];
 
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i)
            L[i] = arr[l + i];
        for (int j=0; j<n2; ++j)
            R[j] = arr[m + 1+ j];
 
 
        /* Merge the temp arrays */
 
        // Initial indexes of first and second subarrays
        int i = 0, j = 0;
 
        // Initial index of merged subarry array
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i] <= R[j])
            {
                arr[k] = L[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                j++;
            }
            k++;
        }
 
        /* Copy remaining elements of L[] if any */
        while (i < n1)
        {
            arr[k] = L[i];
            i++;
            k++;
        }
 
        /* Copy remaining elements of R[] if any */
        while (j < n2)
        {
            arr[k] = R[j];
            j++;
            k++;
        }
    }
 
    // Main function that sorts arr[l..r] using
    // merge()
  public static void sort(int arr[], int l, int r)
    {
        if (l < r)
        {
            // Find the middle point
            int m = (l+r)/2;
 
            // Sort first and second halves
            sort(arr, l, m);
            sort(arr , m+1, r);
 
            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }

 /////////////////////////////////////////////////////////////////////////////////////////
 
	public static int knapsack(int[] weight,int value[],int maxWeight){

        
        int n=  value.length ;
        
	
	//dp[i] stores the profit with KnapSack capacity "i" 
    int []dp = new int[maxWeight+1]; 
      
    //initially profit with 0 to W KnapSack capacity is 0 
    Arrays.fill(dp, 0); 
  
    // iterate through all items 
    for(int i=0; i < n; i++)  
      
        //traverse dp array from right to left 
        for(int j = maxWeight; j >= weight[i]; j--) 
            dp[j] = Math.max(dp[j] , value[i] + dp[j - weight[i]]); 
              
    /*above line finds out maximum of dp[j](excluding ith element value) 
    and val[i] + dp[j-wt[i]] (including ith element value and the 
    profit with "KnapSack capacity - ith element weight") */
    return dp[maxWeight]; 
	}

///////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////


// to return max sum of any subarray in given array
public static long kadanesAlgorithm(long[] arr)
{
      long[] dp = new long[arr.length] ;
      
      dp[0] = arr[0] ;
      long max =  dp[0] ;
      
      
      for(int i = 1; i <  arr.length ; i++)
      {
            if(dp[i-1] > 0)
            {
                  dp[i] = dp[i-1] + arr[i] ;
            }
            else{
                  dp[i] = arr[i] ;
            }
            
            if(dp[i] >  max)max = dp[i] ;
            
      }
      
      return max  ;
      
}
/////////////////////////////////////////////////////////////////////////////////////////////
public static long kadanesAlgorithm(int[] arr)
{
      long[] dp = new long[arr.length] ;
      
      dp[0] = arr[0] ;
      long max =  dp[0] ;
      
      
      for(int i = 1; i <  arr.length ; i++)
      {
            if(dp[i-1] > 0)
            {
                  dp[i] = dp[i-1] + arr[i] ;
            }
            else{
                  dp[i] = arr[i] ;
            }
            
            if(dp[i] >  max)max = dp[i] ;
            
      }
      
      return max  ;
      
}

      
///////////////////////////////////////////////////////////////////////////////////////

// Arrays.sort(arr, new Comparator<Pair>() {
// 			@Override
// 			public int compare(Pair first, Pa second) {
// 				if (first.getAge() != second.getAge()) {
// 					return first.getAge() - second.getAge();
// 				}
// 				return first.getName().compareTo(second.getName());
// 			}
// 		});

/////////////////////////////////////////////////////////////////////////////////////////

public static long binarySerachGreater(int[] arr , int start , int end , int val)
{
      
      // fing total no of elements strictly grater than val in sorted array arr 
      
      
      if(start >  end)return  0 ; //Base case
      
      
      int mid = (start + end)/2  ;
      
      if(arr[mid] <=val)
      {
           return binarySerachGreater(arr,mid+1, end ,val) ; 
            
      }
      else{
            
         return binarySerachGreater(arr,start , mid -1,val) + end-mid+1 ;    
            
      }
      
      
}



//////////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////////


public static void solve()
{
FastReader scn = new FastReader() ;


ArrayList<Integer> list = new ArrayList<>() ;
HashMap<Integer,Integer> map = new HashMap<>() ;
//HashMap<Integer,Integer> map = new HashMap<>() ;
Set<Integer> set = new HashSet<>() ; //Set<Integer> sety = new HashSet<>() ;

int n = scn.nextInt() ;
int w = scn.nextInt() ;

Pair[] arr = new Pair[n] ;

int req = 0;


for(int i = 0 ; i< n; i++)
{
    arr[i] = new Pair() ;
    
    arr[i].first = scn.nextInt() ;
    arr[i].second = i ;
    
    req += (arr[i].first+1)/2 ;
    
   
    
}
    
  if(req > w)out.println(-1) ;
  else{
      
    Arrays.sort(arr, new Comparator<Pair>() {
			@Override
			public int compare(Pair one, Pair two) {
				if (one.first != two.first) {
					return two.first - one.first;
				}
				return two.second-one.second ;
			}
		});
		
		req= w-req ;
		
      int i = 0 ;
      for( ; i < n ;i++)
      {
          
          
          if(req >= (arr[i].first-(arr[i].first+1)/2) )
          {
              arr[i].first = arr[i].first ;
              req = req - (arr[i].first-(arr[i].first+1)/2) ;
          }
          
          else{
              
              arr[i].first = (arr[i].first+1)/2 ;
              arr[i].first += req  ;
              i++;
              
              break ;
              
          }
      }
      
      
      //out.println(req);
      
      for( ;i < n; i++)
      {
          arr[i].first = (arr[i].first+1)/2 ;
      }
      
      int[] array= new int[n] ;
      
      i= 0 ;
      for(;i< n ;i++)
      {
          int index = arr[i].second;
          array[index] = arr[i].first ;
      }
      
      for(Integer x : array)out.print(x+" ");
      
      
  }

    
out.flush() ;  
}


public static void main (String[] args) throws java.lang.Exception
{
  

solve() ;
      
}


}
  
 class Pair 
{
  int first ;
  
  int second  ;
      
@Override
	public String toString() {
	
	String ans = "" ;
	ans  += this.first ;
	ans += " ";
	ans += this.second ;
	
	return ans  ;
	}



}

 