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Unknown Treasure

Time Limit: 1500/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 5082    Accepted Submission(s): 1794


Problem Description
On the way to the next secret treasure hiding place, the mathematician discovered a cave unknown to the map. The mathematician entered the cave because it is there. Somewhere deep in the cave, she found a treasure chest with a combination lock and some numbers on it. After quite a research, the mathematician found out that the correct combination to the lock would be obtained by calculating how many ways are there to pick $m$ different apples among $n$ of them and modulo it with $M$. $M$ is the product of several different primes.
 

Input
On the first line there is an integer $T (T \leq 20)$ representing the number of test cases.

Each test case starts with three integers $n, m, k (1 \leq m \leq n \leq 10^{18}, 1 \leq k \leq 10)$ on a line where $k$ is the number of primes. Following on the next line are $k$ different primes $p_1, . . . , p_k$. It is guaranteed that $M = p_1 , p_2 , , , p_k + 10^{18}$ and $p_i \leq 10^5$ for every $i ( \{1, . . . , k\}$.
 

Output
For each test case output the correct combination on a line.
 

Sample Input
1 9 5 2 3 5
 

Sample Output
6
 

Source
 

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