Number of NKD Sequences

You are given three integers $N$, $K$, and $D$. Count the natural-number sequences $A_1, A_2, \dots, A_K$ of length $K$ that satisfy all of the following conditions.

• $A_1 + A_2 + \dots + A_K = N$
• $A_1 < A_2 < \dots < A_K$
• For every $1 \le i < K$, $A_{i+1} - A_i \le D$
• $A_1 \le D$

The first line contains three integers $N$, $K$, and $D$, separated by spaces.

Print the number of sequences satisfying the conditions, modulo $10^9 + 7$.

• $1 \le N, K, D \le 10^5$