Count Paths in a Grid

You are given an m x n grid. Your task is to determine the number of distinct paths from the top-left corner to the bottom-right corner if you can only move right or down at any step.

The problem can be solved using dynamic programming. Let \(dp[i][j]\) denote the number of ways to reach cell \((i, j)\). The recurrence relation is given by:

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

with the base cases that all cells in the first row and first column have exactly one way to be reached.

For example:

• For a 3x3 grid, the number of paths is 6.
• For a 2x2 grid, the number of paths is 2.

Write a program that reads the grid dimensions from standard input and prints the number of unique paths to standard output.

inputFormat

The input consists of two space-separated integers m and n (1 \le m, n \le 100), representing the number of rows and columns of the grid, respectively. The input is read from standard input (stdin).

outputFormat

The output is a single integer representing the number of distinct paths from the top-left corner to the bottom-right corner in the grid. This should be printed to standard output (stdout).

## sample

3 3

6