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.

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 $1000000007$ ($10^{9} + 7$).

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 $1000000007$ ($10^{9} + 7$).