Problem Statement

You are given a sequence $A=(A_1,A_2,\dots,A_{MK})$ of length $M\times K$ that contains each non-negative integer less than $M$ exactly $K$ times.

You may perform the following operation on the sequence $A$ any number of times (possibly $0$ times).

• Swap $2$ adjacent terms. That is, choose an integer $i$ such that $1\le i\le MK-1$, and swap the values of $A_i$ and $A_{i+1}$.

Find the minimum number of operations required to make the sequence $A$ satisfy the following condition.

• For every integer $i\ (1\le i\le MK-1)$, $A_{i+1} \equiv A_i+1\ (\bmod M)$ holds.

Input

$M\ \ K$
$A_1\ \ A_2\ \ \cdots\ \ A_{MK}$

• $M\ge 2$
• $2 \le M\times K \le 4\times 10^5$
• The sequence $A=(A_1,A_2,\dots,A_{MK})$ contains each non-negative integer less than $M$ exactly $K$ times.
• All input values are integers.

Output

Output the minimum number of operations required to make the sequence $A$ satisfy the condition.

Sample

3 2
1 2 0 2 1 0

1

2 3
0 0 0 1 1 1

3

7 1
3 4 5 6 0 1 2

0