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, ..., A_i, A_i+1,..., A_K) = N
2. LCM (A₁, A₂, ..., A_i, A_i+1,..., A_K) = M
Can you calculate how many kinds of solutions are there for A_i (A_i are all positive numbers).
I began to roll cold sweat but teacher just smiled and smiled. 
Can you solve this problem in 1 minute?