Problem G : Decompose

For any three natural numbers, n, k and x, we call a kx-decomposition of number n a posibility of writing the n number as a sum of k non-null numbers so as the difference between any two terms of the sum to be at least x.

Given three numbers, n,k and x, determine how many distinct kx-decompositions exist. Two decompositions are considered distinct is they differ by at least one term.

Input:

Read from the standard input three non-null natural numbers, n, k and x, separated by one white space.

Output:

Write on the standard output a single value representing the reminder of the division of the number of kx-decompositions by 10007

Notes:

• 20% of the datasets are going to have 0 < n ≤ 200; 80% are going to have 200 < n ≤ 10000

• 1 ≤ x,k ≤ n

• Time limit: 3s

Example