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.ArrayList;
import java.util.Arrays;
import java.util.Collections;

public class Main{
	
	public static void main(String[] args) throws Exception {
		
		int n = nextInt(), b = nextInt();
		int[] a = new int[n];
		double s = 0;
		int max = 0;
		for(int i = 0; i < n; i++){
			a[i] = nextInt();
			s += a[i];
			if(a[i] > max) max = a[i];
		}
		if( (s + b) / n < max) exit("-1");
		double cup = (s + b) / n;
		ArrayList<Double> ans = new ArrayList<Double>();
		for(int i = 0; i < n; i++){
			ans.add(cup - a[i]);
		}
		for(int i = 0; i < n; i++){
			println(ans.get(i));
		}
		
	}
		
	private static PrintWriter out;
	private static BufferedReader inB;
	
	static {
		try {
			out = new PrintWriter(System.out);
			inB = new BufferedReader(new InputStreamReader(System.in));
		} catch(Exception e) {e.printStackTrace();}
	}
	
	private static StreamTokenizer in = new StreamTokenizer(inB);
	
	private static void exit(Object o) throws Exception {
		out.println(o);
		out.flush();
		System.exit(0);
	}
	private static void println(Object o) throws Exception{
		out.println(o);
		out.flush();
	}
	private static void print(Object o) throws Exception{
		out.print(o);
		out.flush();
	}
	private static int nextInt() throws Exception {
		in.nextToken();
		return (int)in.nval;
	}  
	private static String nextString() throws Exception {
		in.nextToken();
		return in.sval;        
	}
}