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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class A implements Runnable {

	private void Solution() throws IOException {
		int n = nextInt(), b = nextInt();
		int[] mas = new int[n];
		int max = 0;
		for (int i = 0; i < n; i++) {
			mas[i] = nextInt();
			max = Math.max(mas[i], max);
		}
		int need = 0;
		for (int i = 0; i < n; i++) {
			need += max - mas[i];
		}
		if (need > b) {
			print("-1");
			return;
		}
		double add = (double) (b - need) / n;
		for (int i = 0; i < n; i++) {
			out.printf("%.6f", max - mas[i] + add);
			println();
		}
	}

	public static void main(String[] args) {
		new A().run();
	}

	BufferedReader in;
	PrintWriter out;
	StringTokenizer tokenizer;

	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			Solution();
			out.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(0);
		}
	}

	void print(Object... o) {
		for (int i = 0; i < o.length; i++) {
			if (i != 0)
				out.print(" ");
			out.print(o[i]);
		}
	}

	void println(Object... o) {
		for (int i = 0; i < o.length; i++) {
			if (i != 0)
				print(" ");
			print(o[i]);
		}
		print("\n");
	}

	int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	long nextLong() throws NumberFormatException, IOException {
		return Long.parseLong(next());
	}

	double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(next());
	}

	String nextLine() throws IOException {
		return in.readLine();
	}

	String next() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens())
			tokenizer = new StringTokenizer(nextLine());
		return tokenizer.nextToken();
	}
}