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 ≤ i ≤ 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 < ... < a_n), or report that it is impossible.

Input

The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ 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 ≤ a_i ≤ 10^9).

Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.

Output

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.

Examples

Input

7 2 1 2 1 1 3 5 1 3 5

Output

4

Input

3 3 1 3 2 1 2 3

Output

-1

Input

5 0 4 3 1 2 3

Output

2

Input

10 3 1 3 5 6 12 9 8 10 13 15 2 4 9

Output

3

inputFormat

Input

The first line contains two integers n and k (1 ≤ n ≤ 5 ⋅ 10^5, 0 ≤ k ≤ 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 ≤ a_i ≤ 10^9).

Then, if k ≠ 0, the third line follows, containing k integers b_1, b_2, ..., b_k (1 ≤ b_1 < b_2 < ... < b_k ≤ n). If k = 0, this line is skipped.

outputFormat

Output

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.

Examples

Input

7 2 1 2 1 1 3 5 1 3 5

Output

4

Input

3 3 1 3 2 1 2 3

Output

-1

Input

5 0 4 3 1 2 3

Output

2

Input

10 3 1 3 5 6 12 9 8 10 13 15 2 4 9

Output

3

样例

7 2
1 2 1 1 3 5 1
3 5

4

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