Score : $1600$ points

Problem Statement

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

You perform the following operation:

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

In how many ways can you give the balls to Snuke? Compute the answer modulo $10^9 + 7$.

Here, we consider two ways to be different if for some $k$, the $k$-th ball given to Snuke has different colors. In particular, the choice of $s, t$ doesn't matter. Also, we don't distinguish two balls of the same color.

Constraints

• $1 \leq A, B \leq 2000$

Input

Input is given from Standard Input in the following format:

$A$ $B$

Output

Print the answer.

3 3

20

There are $20$ ways to give $3$ red balls and $3$ blue balls. It turns out that all of them are possible.

Here is an example of the operation (r stands for red, b stands for blue):

• You choose $s = 3, t = 4$.
• Initially, the row looks like rrrbbb.
• You remove $3$rd ball (r) and give it to Snuke. Now the row looks like rrbbb.
• You remove $4$th ball (b) and give it to Snuke. Now the row looks like rrbb.
• You remove $1$st ball (r) and give it to Snuke. Now the row looks like rbb.
• You remove $3$rd ball (b) and give it to Snuke. Now the row looks like rb.
• You remove $1$st ball (r) and give it to Snuke. Now the row looks like b.
• You remove $1$st ball (b) and give it to Snuke. Now the row is empty.

This way, Snuke receives balls in the order rbrbrb.

4 4

67

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

7 9

7772

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