Unique Paths in a Grid

You are given a grid with dimensions m x n. Starting from the top-left corner (0, 0), you need to reach the bottom-right corner (m-1, n-1) by only moving either down or right at any point in time.

The number of unique paths can be calculated using dynamic programming. Specifically, let \(dp[i][j]\) represent the number of ways to reach the cell at row \(i\) and column \(j\). The recurrence relation is:

\[ dp[i][j] = dp[i-1][j] + dp[i][j-1] \]

with the base conditions \(dp[i][0] = 1\) for all \(i\) and \(dp[0][j] = 1\) for all \(j\). Your task is to compute \(dp[m-1][n-1]\), which is the total number of unique paths from the top-left to the bottom-right corner.

inputFormat

A single line containing two space-separated integers m and n.

outputFormat

Output a single integer which is the number of unique paths from the top-left corner to the bottom-right corner of the grid.## sample

3 7

28