A13962 | Make It Increasing

You are given an array of $n$ integers $a_1$ , $a_2$ , ..., $a_n$ , and a set $b$ of $k$ distinct integers from $1$ to $n$ .

In one operation, you may choose two integers $i$ and $x$ ( $1 \le i \le n$ , $x$ can be any integer) and assign $a_i := x$ . This operation can be done only if $i$ does not belong to the set $b$ .

Calculate the minimum number of operations you should perform so the array $a$ is increasing (that is, $a_1 < a_2 < a_3 < \dots < a_n$ ), or report that it is impossible.

The first line contains two integers $n$ and $k$ ( $1 \le n \le 5 \cdot 10^5$ , $0 \le k \le n$ ) — the size of the array $a$ and the set $b$ , respectively.

The second line contains $n$ integers $a_1$ , $a_2$ , ..., $a_n$ ( $1 \le a_i \le 10^9$ ).

Then, if $k \ne 0$ , the third line follows, containing $k$ integers $b_1$ , $b_2$ , ..., $b_k$ ( $1 \le b_1 < b_2 < \dots < b_k \le n$ ). If $k = 0$ , this line is skipped.

If it is impossible to make the array $a$ increasing using the given operations, print $-1$ .

Otherwise, print one integer — the minimum number of operations you have to perform.