Problem Description

Iroha-chan shouted a string consisting of A and B.

The string contains \(N\\) As and \(M\\) Bs, making it a string of length \(N+M\\), where the first character is A and the last character is B.

It is also known that the string contains the substring AAA (consecutive).

How many possible strings could Iroha-chan have shouted? Find the number of possible strings modulo \(10^9+7\\).

Input Format

The input is given in the following format:

$N\ M$

Output Format

Output the answer in one line.

Sample Input and Output

Sample Input #1

4 3

Sample Output #1

5

Sample Input #2

3 12

Sample Output #2

1

Sample Input #3

2 1000

Sample Output #3

0

Sample Input #4

11451 41919

Sample Output #4

538542250

Notes/Hints

Constraints

• All inputs are integers.
• \(1≦N, M≦10^5\\)

Sample Explanation 1

The strings that satisfy the conditions are AAAABBB, AAABABB, ABBAAAB, AAABBAB, ABAAABB, totaling 5.

Sample Explanation 2

The only string that satisfies the conditions is AAABBBBBBBBBBBB.

Sample Explanation 3

No string satisfies the conditions.

Sample Explanation 4

Output the result modulo \(10^9+7\\).

见题面 Input 部分

见题面 Output 部分