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.

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.