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.util.LinkedList;
import java.util.Locale;

public class Main {

	// split de array
	public static int[ ] atoi( String cad ) {
		String read[] = cad.split( " " );
		int res[] = new int[ read.length ];
		for ( int i = 0; i < read.length; i++ ) {
			res[ i ] = Integer.parseInt( read[ i ] );
		}
		return res;
	}

	public static void main( String[ ] args ) throws IOException {
		BufferedReader in = new BufferedReader( new InputStreamReader( System.in ) );
		String line = in.readLine( );
		int dates[] = atoi( line );
		int arr[] = atoi( in.readLine( ) );
		int p = -1;
		for ( int i = 0; i < arr.length; i++ ) {
			if ( arr[ i ] > p )
				p = arr[ i ];
		}
		LinkedList<Float> lista = new LinkedList<Float>( );

		for ( int i = 0; i < arr.length; i++ ) {
			lista.add( (float) (p - arr[ i ]) );
			dates[ 1 ] -= (float) (p - arr[ i ]);
		}
		if ( dates[ 1 ] < 0 ) {
			System.out.println( -1 );
		} else {
				for ( int i = 0; i < lista.size( ); i++ ) {
					System.out.printf( Locale.UK,"%.6f",(lista.get( i )+(float)dates[1]/dates[0]) );
					System.out.println();

				}	
		}

	}

}