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.Scanner;
import java.util.Arrays;
public class ProblemAboutEquation {
	
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		
		int n = scan.nextInt();
		int b = scan.nextInt();
		double array[] = new double[n];
		double ans[] = new double[n];
		double max = 0;
		for (int i = 0; i < n; i++) {
			array[i] = scan.nextInt();
			if (array[i]>max) max = array[i];
		}
		boolean imp = false;
		for (int i = 0; i < n; i++) {
			double newNum = max-array[i];
			b -= newNum;
			if(b>=0){
				array[i] = newNum+array[i];
				ans[i] = newNum;
			} else {
				imp = true;
				break;
			}
		}
		
		if(!imp){
			double div = b / (double)n;
			for (int i = 0; i < n; i++) {
				ans[i] += div;
				ans[i] = (double)Math.round(ans[i] * 1000000d) / 1000000d;
				System.out.println(String.format("%.6f",ans[i]));
			}
		} else {
			System.out.println(-1);
		}
		
	}

}