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 (10^{9} + 7).

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