Score : $800$ points

Problem Statement

Snuke has a string $x$ of length $N$. Initially, every character in $x$ is 0.

Snuke can do the following two operations any number of times in any order:

• Choose $A$ consecutive characters in $x$ and replace each of them with 0.
• Choose $B$ consecutive characters in $x$ and replace each of them with 1.

Find the number of different strings that $x$ can be after Snuke finishes doing operations. This count can be enormous, so compute it modulo $(10^9+7)$.

Constraints

• $1 \leq N \leq 5000$
• $1 \leq A,B \leq N$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $A$ $B$

Output

Print the number of different strings that $x$ can be after Snuke finishes doing operations, modulo $(10^9+7)$.

4 2 3

11

For example, $x$ can be 0011 or 1111 in the end, but cannot be 0110.

10 7 2

533

1000 100 10

828178524