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.text.*; import java.io.BufferedReader;import java.math.*; import java.util.regex.*; import java.awt.geom.*; import static java.lang.Math.*; import static java.lang.Character.*; import static java.lang.Integer.*; import static java.lang.Double.*; import static java.lang.Long.*; import static java.lang.System.*; import static java.util.Arrays.*;

import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;

public class A {
    static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    static PrintStream out = System.out;

    static int n, b;
    static int[]a;
	static void readInput() throws IOException {
		int[]x = parseArrInt(in.readLine());
		n = x[0]; b = x[1];
		a = parseArrInt(in.readLine());
	}

	static void process() {
		double sum = b;
		for (int i = 0; i < n; i++) sum += a[i];
		double equal = sum / n;
		boolean ok = true;
		for (int i = 0; i < n; i++) {
			if (equal + 1e-7 < a[i]) ok = false;
		}
		if (!ok) {
			System.out.println(-1);
			return;
		}
		
		for (int i = 0; i < n; i++) {
			System.out.format("%.7f%n", equal - a[i]);
		}
	}

	public static void main(String[] args) throws IOException {
		readInput();
		process();
	}

	public static void debug(Object...os) { 
		System.err.println(Arrays.deepToString(os));
	} 
	static int[] parseArrInt(String s) {
		StringTokenizer st = new StringTokenizer(s);
		int count = 0;
		int[] temp = new int[100], res;
		while (st.hasMoreTokens()) {
			temp[count++] = Integer.parseInt(st.nextToken());
		}
		res = new int[count];
		for (int i = 0; i < count; i++) {
			res[i] = temp[i];
		}
		return (res);
	}

}