You are given an array \(A\) of \(N\) integers. You can perform following operations :

• Choose two distinct indices \(i\) and \(j\), increment \(A_i\) by \(1\) and decrement \(A_j\) by \(1\)

Find the minimum number of operations you should perform such that absolute difference between any two elements is at most \(K\) 

Input Format:

The First line contains two integers \(N\) and \(K\) .

The second line contains the \(N\) elements of array \(A\) .

Output Format

Print the minimum number of operations.

Constraints

\(1 \leq N \leq 10^5 \\ 1 \leq K \leq 10^9 \\ 1 \leq A_i \leq 10^5\)