Number of paths in a grid 2

Given a grid of height h and width w, you are asked to calculate the number of unique paths one can take to move from the top-left corner to the bottom-right corner. You’re only allowed to move right, down, and diagonally in the bottom-right direction.
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Input

The input contains two integers h and w (1 ≤ h, w ≤ 100).

Output

The program should print the number of unique paths it’s possible to take from the top-left to the bottom-right corner of the grid. The output can be large, so the answer should be taken modulo .

Examples

Input
Output
2 3
5
3 4
25
 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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