Problem: A group of n merry programmers celebrate Robert Floyd's birthday. Polucarpus has got an honourable task of pouring Ber-Cola to everybody. Pouring the same amount of Ber-Cola to everybody is really important. In other words, the drink's volume in each of the n mugs must be the same.

Polycarpus has already began the process and he partially emptied the Ber-Cola bottle. Now the first mug has a1 milliliters of the drink, the second one has a2 milliliters and so on. The bottle has b milliliters left and Polycarpus plans to pour them into the mugs so that the main equation was fulfilled.

Write a program that would determine what volume of the drink Polycarpus needs to add into each mug to ensure that the following two conditions were fulfilled simultaneously: 

  * there were b milliliters poured in total. That is, the bottle need to be emptied; 
  * after the process is over, the volumes of the drink in the mugs should be equal. 

Input

The first line contains a pair of integers n, b (2 ≤ n ≤ 100, 1 ≤ b ≤ 100), where n is the total number of friends in the group and b is the current volume of drink in the bottle. The second line contains a sequence of integers a1, a2, ..., an (0 ≤ ai ≤ 100), where ai is the current volume of drink in the i-th mug.

Output

Print a single number "-1" (without the quotes), if there is no solution. Otherwise, print n float numbers c1, c2, ..., cn, where ci is the volume of the drink to add in the i-th mug. Print the numbers with no less than 6 digits after the decimal point, print each ci on a single line. Polycarpus proved that if a solution exists then it is unique.

Russian locale is installed by default on the testing computer. Make sure that your solution use the point to separate the integer part of a real number from the decimal, not a comma.

Examples

Input

5 50
1 2 3 4 5


Output

12.000000
11.000000
10.000000
9.000000
8.000000


Input

2 2
1 100


Output

-1

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class A
{
    BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = null;
    
    private void solve() throws IOException
    {
        int n = nextInt();
        int b = nextInt();
        double a[] = new double[n];
        double s = b;
        for(int i = 0; i < n; i++)
        {
            a[i] = nextInt();
            s += a[i];
        }
        
        s = s / n;
        boolean is = true;
        for(int i = 0; i < n; i++)
        {
            a[i] = s - a[i];
            if(a[i] < 0)
            {
                is = false;
            }
            
        }
        
        if(is)
        {
            for(int i = 0; i < n; i++)
            {
                System.out.print(a[i] + " ");
            }
        }
        else
        {
            System.out.println(-1);
        }
        
    }
    
    String nextToken() throws IOException
    {
        if (st == null || !st.hasMoreTokens())
        {
            st = new StringTokenizer(bf.readLine());
        }
        
        return st.nextToken();
    }

    int nextInt() throws IOException
    {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException
    {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException
    {
        return Double.parseDouble(nextToken());
    }

    public static void main(String args[]) throws IOException
    {
        new A().solve();
    }
    
}