Path Through an Asteroid Field

You are given a grid represented as an n x m matrix, where each cell is either safe or contains an asteroid. A cell is safe when its value is 0 and contains an asteroid when its value is 1. The top-left cell is at position (1,1) and the bottom-right cell is at (n,m). Your task is to determine if there exists a path from the top-left cell to the bottom-right cell, moving only right or down, that does not pass through any asteroids.

Formally, given the matrix \(G\) where \(G_{i,j}\) is defined as above, determine if there exists a sequence of moves beginning at \(G_{1,1}\) and ending at \(G_{n,m}\) such that each move is either to the right or down, and every visited cell \(G_{i,j}\) satisfies \(G_{i,j} = 0\).

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

inputFormat

The first line contains two integers n and m (1 ≤ n, m ≤ 1000), 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 the grid. A value of 0 means the cell is safe, and 1 means the cell contains an asteroid.

outputFormat

Output a single line with the string YES if there exists a valid path from the top-left corner to the bottom-right corner, or NO otherwise.

3 3
0 1 0
0 0 0
1 0 0

YES