Description
Yanghui Triangle, as known as Pascal’s Triangle, is a number triangle with numbers arranged in staggered row such that
an, 0 = 1 (n ≥ 0)
an, n = 1 (n ≥ 0)
an, r = an − 1, r − 1 + an − 1, r (0 < r < n)
Consider a decimal number p with sequentially consists of k-digit decimal representations of the numbers in the n-th row of Yanghui Triangle where log10 an, r < k for all 0 ≤ r ≤ n. Here are some examples:
n k p
0 1 1
3 2 01030301
5 2 010510100501
The numerical value of p can be very large. Your task is to calculate p mod m for some integer m.
Input
The input consists of T test cases. The number of test cases T is given in the first line of the input file. Each test case consists of one line containing n, k, m (0 ≤ n ≤ 1 000 000, 1 ≤ k ≤ 1 000 000, 2 ≤ m ≤ 109) in order.
Output
The output should contain p mod m, one per line.
Sample Input
3
0 2 7
2 2 12345
5 2 1000000
Sample Output
1
10201
100501
