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.util.*;
import java.io.*;



public class a {
	
	public static void main(String agrs[]){
		Scanner in = new Scanner(System.in);
		
		
		int n = in.nextInt();
		int b =in.nextInt();
		int max = 0;
		int sum = 0;
		int a[] = new int[n];
		for (int i = 0; i<n; i++){
			a[i] = in.nextInt();
			max = Math.max(max, a[i]);
			sum += a[i];
		}
		
		int b2 = sum  + b;
		
		int ans = 0;
		if (b2/n >= max){
				for (int i = 0; i<n; i++){
					//print((double)b2/n - a[i]);
					System.out.printf("%.6f", ((double)b2/n - a[i]));
					System.out.println();
				}
		}else {
			System.out.println(-1);
		}
	}
	/*
	static void print(double a){
		String s = (a + 1e-7) +"";
		int i = s.indexOf(".");
		for (int i = i<s.length(); i++)
			{}
		s = s.substring(0, s.length() - 6) + "." + (s.substring(s.length() - 6, s.length()));
		System.out.println(s);
	}*/

}