Problem Description

There are $ A + B $ balls arranged in a row. The leftmost $ A $ balls are red, and the rightmost $ B $ balls are blue.

You perform the following operations:

• First, choose integers $ s, t $ such that $1 \leq s, t \leq A + B$.
• Then, repeat the following steps $ A + B $ times: In each step, you choose the first ball from the left, or the $ s $-th ball (if it exists), or the $ t $-th ball (if it exists, all 1-based) and give it to Snuke.

How many ways can you give the balls to Snuke? Find the answer modulo $ 10^9 + 7 $.

Here, two methods are considered different if, for some integer $ k $, the color of the $ k $-th ball given to Snuke is different. Notably, the choice of $ s, t $ does not matter. Also, two balls of the same color are indistinguishable.

Input Format

The input is given from the standard input in the following format:

$ A $ $ B $

Output Format

Output the answer.

Sample Input and Output

Sample Input #1

3 3

Sample Output #1

20

Sample Input #2

4 4

Sample Output #2

67

Sample Input #3

7 9

Sample Output #3

7772

Sample Input #4

1987 1789

Sample Output #4

456315553

Notes/Hints

Constraints

• $1 \leq A, B \leq 2000$

Sample Explanation 1

There are $ 20 $ ways to give $ 3 $ red balls and $ 3 $ blue balls. It can be seen that all these methods are possible. Here is an example of the operation (r represents red, b represents blue): - Choose $ s = 3, t = 4 $. - Initially, the row is rrrbbb. - Remove the $ 3 $-th ball (r) and give it to Snuke. The row is now rrbbb. - Remove the $ 4 $-th ball (b) and give it to Snuke. The row is now rrbb. - Remove the $ 1 $-st ball (r) and give it to Snuke. The row is now rbb. - Remove the $ 3 $-th ball (b) and give it to Snuke. The row is now rb. - Remove the $ 1 $-st ball (r) and give it to Snuke. The row is now b. - Remove the $ 1 $-st ball (b) and give it to Snuke. The row is now empty. In this method, Snuke receives the balls in the order rbrbrb.

Sample Explanation 2

There are $ 70 $ ways to give $ 4 $ red balls and $ 4 $ blue balls. Among them, only bbrrbrbr, brbrbrbr, brrbbrbr are impossible.

见题面 Input 部分

见题面 Output 部分