B'Some permutation of length n is guessed. You are given the indices of its prefix maximums and suffix maximums. Recall that a permutation of length k is an array of size k such that each integer from 1 to k occurs exactly once. Prefix maximums are the elements that are the maximum on the prefix ending at that element. More formally, the element a_i is a prefix maximum if a_i > a_j for every j < i . Similarly, suffix maximums are defined, the element a_i is a suffix maximum if a_i > a_j for every j > i . You need to output the number of different permutations that could have been guessed. As this number can be very large, output the answer modulo 10^9 + 7 . Each test consists of several test cases. The first line contains a single integer t ( 1 <= t <= 10^4 ) -- the number of test cases. Then follows the description of the test cases. The first line of each test case contains three integers n, m_1 and m_2 ( 1 <= m_1, m_2 <= n <= 2 cdot 10^5 ) -- the length of the permutation, the number of prefix maximums, and the number of suffix maximums, respectively. The second line of each test case contains m_1 integers p_1 < p_2 < ldots < p_{m_1} ( 1 <= p_i <= n ) -- the indices of the prefix maximums in increasing order. The third line of each test case contains m_2 integers s_1 < s_2 < ldots < s_{m_2} ( 1 <= s_i <= n ) -- the indices of the suffix maximums in increasing order. It is guaranteed that the sum of the values of n for all test cases does not exceed 2 cdot 10^5 . For each test case, output a single integer on a separate line -- the number of suitable permutations modulo 10^9 + 7 . The following permutations are suitable for the second set of input data: The following permutations are suitable for the sixth set of input data: '...