Math Magic

Time Limit: Java: 3000 ms / Others: 3000 ms

Memory Limit: Java: 32768 KB / Others: 32768 KB


Yesterday, my teacher taught us about math: +, -, *, /, GCD, LCM... As you know, LCM (Least common multiple) of two positive numbers can be solved easily because of a * b = GCD (a, b) * LCM (a, b).

In class, I raised a new idea: "how to calculate the LCM of K numbers". It's also an easy problem indeed, which only cost me 1 minute to solve it. I raised my hand and told teacher about my outstanding algorithm. Teacher just smiled and smiled...

After class, my teacher gave me a new problem and he wanted me solve it in 1 minute, too. If we know three parameters N, M, K, and two equations:

1. SUM (A1, A2, ..., Ai, Ai+1,..., AK) = N
2. LCM (A1, A2, ..., Ai, Ai+1,..., AK) = M

Can you calculate how many kinds of solutions are there for Ai (Ai are all positive numbers). I began to roll cold sweat but teacher just smiled and smiled.

Can you solve this problem in 1 minute?


There are multiple test cases.

Each test case contains three integers N, M, K. (1 ≤ N, M ≤ 1,000, 1 ≤ K ≤ 100)


For each test case, output an integer indicating the number of solution modulo 1,000,000,007(1e9 + 7).

You can get more details in the sample and hint below.

Sample Input

4 2 2
3 2 2

Sample Output



The first test case: the only solution is (2, 2).

The second test case: the solution are (1, 2) and (2, 1).


The 2012 ACM-ICPC Asia Changchun Regional Co