In the popular TV series Heroes, there is a tagline "Save the cheerleader, Save the world!". Here Heroes continues, "Solve the puzzle, Save the world!".
Finally, alien invaders visit our planet. They are eccentric and launch attack many rounds. Since trust in prime numbers, each round they send out p killers, here p is a prime number. Countries on our planet unite and assemble an armed troop of n population. And fortunately we get a fatal weakness of enemy from a betrayer. If the ways of choosing m warriors from n is a multiple of p, the killer number, we will win. Otherwise, we will lose. As the greatest programmer of our planet, you are invited to write a program to count the number of m(0≤m≤n) such that C(n, m) is a multiple of prime p.