You have a sequence $a$ with length $N$ created by removing some elements (possibly zero) from a permutation of numbers $(1, 2, \dots, N)$. When an element is removed, the length of the sequence doesn't change, but there is an empty spot left where the removed element was. You also have an integer $K$.
Let's call a permutation $p_1, p_2, \dots, p_N$ good if:
- it is possible replace empty spots in $a$ by numbers in such a way that we obtain the permutation $p$
- the number of positions $i$ ($1 < i \le N$) such that $p_i > p_{i-1}$ is equal to $K$
Your task is to find the number of good permutations.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two space-separated integers $N$ and $K$.
- The second line contains $N$ space-separated integers $a_1, a_2, \dots, a_N$. Each element of this sequence is either $0$ (indicating an empty spot previously occupied by a removed element) or an integer between $1$ and $N$ inclusive.

-----Output-----
For each test case, print a single line containing one integer — the number of good permutations.

-----Constraints-----
- $1 \le T \le 300$
- $0 \le K < N \le 8$
- each integer between $1$ and $N$ inclusive appears in $a$ at most once

-----Example Input-----
1
3 1
2 0 0

-----Example Output-----
2

-----Explanation-----
Example case 1: The two possible good permutations are $(2,3,1)$ and $(2,1,3)$.

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