Given an array a consisting of n elements, call array b consisting of n elements such that (a[1] — b[1])^2 + (a[2] — b[2])^2 + ... + (a[n] — b[n])^2 is minimum and sum of all elements of array B is equal to m.

Given n, array A, m, find the value of (a[1] — b[1])^2 + (a[2] — b[2])^2 + ... + (a[n] — b[n])^2.

Constraints : 1 <= n <= 1e5 , 1 <= m <= 2e9, 1 <= a[i] <= 2e9

Input : first line n,m respectively, second line is the elements of array A Output : the expected value

Ex:

Input : 3 3
        3 4 5
Output : 27
Input : 10 4
        2 3 4 5
Output : 4