
ZOJ Problem Set  2867
Bob has a set {1, 2, ..., N}, and he want to choose a subset with exactly M numbers. For a subset S, if it contains both x and Kx, then S is bad, otherwise S is good, where K is a given number. Given N, M and K, Bob wants to know how many good subsets with exact M numbers he can choose. InputThere are multiple test cases. The first line of input contains an integer T indicating the number of test cases. For each test case: There is only one line contain three integers N, M and K (1 <= N <= 10^{9}, 1 <= M, K <= 100). OutputFor each test case, output the number of ways to choose a good subset with exact M numbers. The number may be too large, output it modulo 12347. Sample Input3 3 2 3 6 3 2 10 2 3 Sample Output2 9 42 HintFor sample 1, only {2, 3} and {1, 2} are good subset. For sample 2, those 9 subsets are good: {1, 3, 4}, {1, 3, 5}, {1, 4, 5}, {1, 4, 6}, {1, 5, 6}, {2, 3, 5}, {2, 5, 6}, {3, 4, 5} and {4, 5, 6}. For sample 3, except {1, 3}, {3, 9} and {2, 6}, all the other 42 subset are good. 