Let's consider a permutation P = {$p_{1}$,$ p_{2}$, ..., $p_{N}$} of the set of N = {1, 2, 3, ..., N} elements .

P is called a magic set if it satisfies both of the following constraints:

Given a set of K integers, the elements in positions $a_{1}$, $a_{2}$, ..., $a_{K}$ are less than their adjacent elements, i.e., $p_{ai-1} > p_{ai} < p_{ai+1}$
Given a set of L integers, elements in positions $b_{1}$, $b_{2}$, ..., $b_{L}$ are greater than their adjacent elements, i.e., $p_{bi-1} < p_{bi} > p_{bi+1}$

How many such magic sets are there?

Input Format

The first line of input contains three integers N, K, L separated by a single space.

The second line contains K integers, $a_{1}$, $a_{2$}, ... $a_{K}$ each separated by single space.

the third line contains L integers, $b_{1}$, $b_{2}$, ... $b_{L}$ each separated by single space.

Output Format

Output the answer modulo 1000000007 (10^{9}+7).

Constraints

3 <= N <= 5000

1 <= K, L <= 5000

2 <= $a_{i}$, $b_{j}$ <= N-1, where i ∈ [1, K] AND j ∈ [1, L]

Sample Input #00

4 1 1
2
3

Sample Output #00

5

Explanation #00

Here, N = 4 $a_{1}$ = 2 and $b_{1}$ = 3. The 5 permutations of {1,2,3,4} that satisfy the condition are

2 1 4 3
3 2 4 1
4 2 3 1
3 1 4 2
4 1 3 2

Sample Input #01

10 2 2
2 4
3 9

Sample Output #01

161280

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