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).

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).

Constraints

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

Sample Input 1

4 2 3

Sample Output 1

11

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

Sample Input 2

10 7 2

Sample Output 2

533

Sample Input 3

1000 100 10

Sample Output 3

828178524

见题面 Input 部分

见题面 Output 部分