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.PrintStream;
import java.util.Arrays;
import java.util.InputMismatchException;

/**
 * 
 * @author Code Forces.  Solution by: L.Azuaje.
 *
 * Problem: .
 *
 *
 */

public class Main {
    public  Main() {
    }

    public static int findMaxIndex(int[] array) {
        int index = -1;
        int max = 0;

        for (int i = 0; i < array.length; i++) {
            if (array[i] >= max) {
                max = array[i];
                index = i;
            }
        }

        return index;
    }

	public static void main(String[] args) throws IOException {
        FastInputReader scanner = new FastInputReader();
        PrintStream out = System.out;

        int[] data = scanner.nextIntArray(2);
        int[] data2 = scanner.nextIntArray(data[0]);

        double[] solution = new double[data[0]];

        double sum = data[1];

        // Find max index
        int maxIndex = findMaxIndex(data2);
        int max = data2[maxIndex];

        int total = 0;
        for (int i = 0; i < data2.length; i++) {
            total += max - data2[i];
         }

         if (total <= data[1]) {
             data[1] -= total;
             sum = sum - total;
             for (int i = 0; i < data2.length; i++) {
                 solution[i] = max;
             }

             for (int i = 0; i < data2.length; i++) {
                 solution[i] += sum / data[0];
                 out.format("%f %n", solution[i] - data2[i]);
             }

         } else {
             out.println(-1);
         }

		out.close();
	}

	// -----------MyScanner class for faster input----------
    public static class FastInputReader {
        private byte[] buf = new byte[16384];
        private int    curChar;
        private int    numChars;

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = System.in.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }

	public static class MyScanner {
		BufferedReader reader;

		public MyScanner() {
			this.reader = new BufferedReader(new InputStreamReader(System.in));
		}

		public void close() throws IOException {
			this.reader.close();
		}

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

		long nextLong() {
			return Long.parseLong(this.next());
		}

        float nextFloat() {
            return Float.parseFloat(this.next());
        }

        double nextDouble() {
            return Double.parseDouble(this.next());
        }

        String next() {
			String str = "";
			try {
				str = this.reader.readLine().trim();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		String[] nextStringArray() {
			String[] str = null;
			try {
				str = this.reader.readLine().trim().split(" ");
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		int[] nextIntArray() {
			String[] data  = nextStringArray();
			int[] a  = new int[data.length];

			for (int i = 0; i < a.length; i++) {
				a[i] = Integer.parseInt(data[i]);
			}

			return a;
		}

		Integer[] nextIntegerArray() {
			String[] data  = nextStringArray();
			Integer[] a  = new Integer[data.length];

			for (int i = 0; i < a.length; i++) {
				a[i] = Integer.parseInt(data[i]);
			}

			return a;
		}

		long[] nextLongArray() {
			String[] data  = nextStringArray();
			long[] a  = new long[data.length];

			for (int i = 0; i < a.length; i++) {
				a[i] = Long.parseLong(data[i]);
			}

			return a;
		}

        float[] nextFloatArray() {
            String[] data  = nextStringArray();
            float[] a  = new float[data.length];

            for (int i = 0; i < a.length; i++) {
                a[i] = Float.parseFloat(data[i]);
            }

            return a;
        }

        double[] nextDoubleArray() {
            String[] data  = nextStringArray();
            double[] a  = new double[data.length];

            for (int i = 0; i < a.length; i++) {
                a[i] = Double.parseDouble(data[i]);
            }

            return a;
        }
    }
}