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Description

給你一個 $N \times M$ 的棋盤

令左上角為 $(1, 1)$ ，右下角為 $(N, M)$

如果從 $(1, 1)$ 開始，只能往右或往下走

試問有幾種相異的走法可以走到 $(N, M)$

請將答案模 $10^{9} + 7$ 輸出

Input Format

$N$ $M$

$1 \leq N, M \leq 2000$

Output Format

輸出一非負整數

Sample Input 1

2 2

Sample Output 1

Sample Input 2

2 3

Sample Output 2

Hints

範例測資2的圖形有以上三種走法

Subtasks

No.	Testdata Range	Score

TopCoder

807

$學長對不起$

User's AC Ratio

85.7% (30/35)

Tags

Low DP

Problem Source

經典題 Path on Grid

Testdata and Limits

No.	Time Limit (ms)	Memory Limit (VSS, KiB)	Memory Limit (RSS, KiB)	Output Limit (KiB)	Subtasks
0	1000	250000	250000	65536
1	1000	250000	250000	65536
2	1000	250000	250000	65536
3	1000	250000	250000	65536
4	1000	250000	250000	65536
5	1000	250000	250000	65536
6	1000	250000	250000	65536

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