An LED strip has n cells in a line, each ON or OFF. To keep the animation lively, the strip must never contain a run of a or more consecutive ON cells, and never a run of b or more consecutive OFF cells. Count how many distinct patterns of length n satisfy both rules. Report the count modulo 1000000007.
Input format
A single line with three integers n, a, and b.
Output format
A single integer: the number of valid patterns, modulo 1000000007.
Constraints
- 1 <= n <= 18
- 1 <= a <= 20
- 1 <= b <= 20