Problem Statement

You are given an integer sequence $A=(A_1,A_2,\dots,A_N)$ of length $N$.

You can rearrange $A$ freely. Find the maximum value that $\sum_{i=1}^{N-1} ((A_{i+1} - A_i) \bmod K)$ can take after rearranging.

Here, $x \bmod K$ denotes the integer $y$ such that $0 \le y < K$ and $x - y$ is a multiple of $K$. For example, $-3 \bmod 8 = 5$, and $9 \bmod 6 = 3$.

Constraints

• $2 \le N \le 2 \times 10^5$
• $1 \le K \le 10^9$
• $0 \le A_i < K$

Input

The input is given from Standard Input in the following format:

N K
A_1 A_2 \dots A_N

Output

Print the answer.