A8545 | Problem About Equation

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 $a_{1}$ 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.

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.

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.