Unique Paths

A robot stands at the top-left cell of a rows x cols grid and moves only right or down to reach the bottom-right cell. Return the number of different paths. Return the answer modulo 10**9 + 7.

For rows = 3 and cols = 7 the answer is 28.

The starter code is a plain recursion. It is correct but too slow for big grids.

Examples

Example 1

Input:

unique_paths(3, 7)

Output:

28

Example 2

Input:

unique_paths(3, 2)

Output:

3

Constraints

• 1 <= rows, cols <= 1000