Drawing a Path in a Grid

You are given an n × m grid consisting of integers 0 and 1. A cell containing 0 is walkable, whereas a cell with 1 is blocked. Starting from the top-left cell at position \((0,0)\), you can only move either to the right (i.e. \((i, j+1)\)) or downward (i.e. \((i+1, j)\)). Your task is to determine whether there exists a valid path from the top-left cell to the bottom-right cell at position \((n-1, m-1)\).

If a valid path exists, output YES; otherwise, output NO.

inputFormat

The first line contains two integers, \(n\) and \(m\), representing the number of rows and columns of the grid, respectively.

Each of the next \(n\) lines contains \(m\) space-separated integers (each either 0 or 1) representing a row of the grid.

outputFormat

Output a single line containing either YES if a valid path exists, or NO if it does not.

## sample

3 3
0 1 0
0 0 0
0 1 0

YES

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