Escape the Room

You are trapped in a room represented by an m x n matrix. Each cell of the matrix contains a positive integer. We denote the cell on the x-th row and y-th column as (x,y) (1-indexed).

You start from cell (1,1) and your goal is to reach cell (m,n). From a cell containing the number \(num\), you can jump to a cell (x,y) if and only if \(x \times y = num\). For example, if you are in a cell containing \(6\), you may jump to (2,3) (or (3,2) if within bounds) because \(2 \times 3 = 6\>.

Determine whether you can escape the room by reaching cell (m,n) following the above rules.

inputFormat

The first line contains two integers m and n (\(1 \leq m,n\leq 1000\), for example), representing the number of rows and columns of the matrix. Each of the next m lines contains n positive integers, representing the grid. Note that the matrix is 1-indexed.

outputFormat

Output yes if it is possible to escape the room, or no otherwise.

sample

3 4
3 10 8 14
1 11 12 12
6 2 3 9

yes