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.*;


import java.util.*;


public class A {	
	static void finish(){
		System.out.println(-1);
		System.exit(0);
	}
	
	static boolean f(double q1,double q2){
		double yed = q1/q2;
		if (Math.abs(yed-Math.round(yed))<=1e-9) return true;
		return false;
	}
public static void main(String args[]) throws Exception{
	Scanner in =  new Scanner(System.in);
	int n=in.nextInt();double k =in.nextInt(),max=0;
	int[] a = new int[101];double[] d = new double[101];
	for (int i=1;i<=n;i++) {a[i]=in.nextInt();if (a[i]>max) max = a[i];}
	
	for (int i=1;i<=n;i++)
		if (k>=max-a[i]) {k-=(max-a[i]);d[i] = max-a[i];} else finish();
	
	//if (k>0 && !f(k,n)) finish(); else {
		for (int i=1;i<=n;i++) d[i]+=k/n;
	
		
		
		for (int i=1;i<=n;i++)
			System.out.printf("%.6f\n",d[i]);
		
 }
}