【cf431C】k-Tree

2014年5月22日1,1280

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.

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.

 

 

As soon as Dima, a good friend of Lesha, found out about the tree, he immediately wondered: “How many paths of total weight n (the sum of all weights of the edges in the path) are there, starting from the root of a k-tree and also containing at least one edge of weight at least d?”.Help Dima find an answer to his question. As the number of ways can be rather large, print it modulo 1000000007 (109 + 7).

Input

A single line contains three space-separated integers: nk and d (1 ≤ n, k ≤ 100; 1 ≤ d ≤ k).

Output

Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).

Sample test(s)
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题解

一棵树每个有k个儿子,边权为1-k

问你有多少条从根开始的路径,边权和为n,最小边大于d

此题跟树似乎没有任何关系

f[i][j]表示和为i最小值为j的方案数

f[i+k][max(j,k)]+=f[i][j]