#P431C. k-Tree
k-Tree
No submission language available for this problem.
Description
Quite recently a creative student Lesha had a lecture on trees. After the lecture Lesha was inspired and came up with the tree of his own which he called a k-tree.
A k-tree is an infinite rooted tree where:
- each vertex has exactly k children;
- each edge has some weight;
- if we look at the edges that goes from some vertex to its children (exactly k edges), then their weights will equal 1, 2, 3, ..., k.
The picture below shows a part of a 3-tree.
Help Dima find an answer to his question. As the number of ways can be rather large, print it modulo 1000000007 (109 + 7).
A single line contains three space-separated integers: n, k and d (1 ≤ n, k ≤ 100; 1 ≤ d ≤ k).
Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).
Input
A single line contains three space-separated integers: n, k and d (1 ≤ n, k ≤ 100; 1 ≤ d ≤ k).
Output
Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).
Samples
3 3 2
3
3 3 3
1
4 3 2
6
4 5 2
7