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A. Problem About Equation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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 *a*_{1} milliliters of the drink, the second one has *a*_{2} 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 *a*_{1}, *a*_{2}, ..., *a*_{n} (0 ≤ *a*_{i} ≤ 100), where *a*_{i} 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 *c*_{1}, *c*_{2}, ..., *c*_{n}, where *c*_{i} 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 *c*_{i} 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

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