TripleK#1468
"Do not worry about your problems with mathematics, I assure you mine are far greater."
Albert Einstein
Residents of planet MCA love candies. Koosha and Kaveh are MCA residents. But they do not love candies more than each other. Keivan captured many candies as trophies in a war against ACM planet's residents. Now, as the owner of many candies, he wants to divide them between Koosha and Kaveh. Considering that if either of them eats more than candies and gets a toothache, Keivan decides to divide the candies so that neither of them receives more than candies. Koosha and Kaveh trust Keivan with the division, as they know that each will receive at least one candy, and friendship is more valuable than candies!
However, there is another problem the trio must solve. Koosha and Kaveh have the same number of packets in their clothes, and each packet must contain the same number of candies. Otherwise, their balance might be disturbed while walking, and they may not be able to move.
For example, suppose Keivan wants to divide candies between Koosha and Kaveh, and each person can receive at most candies. Each has packets. In this case, there are possible ways to divide the candies: Koosha gets candies and Kaveh gets , or vice versa. If there are candy lovers, finding the number of possible divisions is easy, but TripleK (Keivan, Kaveh, and Koosha) want to solve the problem for any number of candy lovers, any number of candies, any maximum number, and any number of packets.
The input consists of several test cases. Each test case is on a separate line, with the numbers separated by spaces. The first number is the number of candies (0 < m \leq 60). The second number is the number of candy lovers (0 < n \leq m). The third number is the maximum number of candies one person can receive (0 < p \leq m). All people have packets in their clothes (k \leq m and m \bmod k = 0). These people love candies so much that they may have quite a lot of packets. Receiving candies is not a surprise for them!
For each line of input, output a single integer in a separate line indicating the number of ways to divide all candies among the candy lovers.
Example 1