You are given an integer sequence $A=[A_1,A_2,\ldots,A_N]$ of length $N$ and an integer $K$.

You can perform the following operation as many times as you want. (Possibly, zero)

• Choose an integer $i$ satisfying $1\le i\le N$, and change $A_i$ to $A_i+K$. Note that if $K<0$, this operation is equivalent to subtracting $\vert{}K\vert{}$ from $A_i$.

Your goal is to make the sequence satisfy the following condition.

Find the minimum number of operations required.

The input is given in the following format.

$N\ K$ $A_1\ A_2\ \cdots \ A_N$

Print the minimum number of operations required to satisfy the given condition.

• $1 \le N \le 200\ 000$.
• $1 \le \vert{}K\vert{} \le 1 \ 000 \ 000 \ 000$.
• $0 \le \vert{}A_i\vert{} \le 1 \ 000 \ 000 \ 000$ ($1 \leq i \leq N$).