Canadian Computing Competition: 2020 Stage 1, Junior #5, Senior #2

You have to determine if it is possible to escape from a room. The room is an ~M~-by-~N~ grid with each position (cell) containing a positive integer. The rows are numbered ~1, 2, ..., M~ and the columns are numbered ~1, 2, ..., N~. We use ~(r, c)~ to refer to the cell in row ~r~ and column ~c~.

You start in the top-left corner at ~(1, 1)~ and exit from the bottom-right corner at ~(M, N~. If you are in a cell containing the value ~x~, then you can jump to any cell ~(a, b)~ satisfying ~a \times b = x~. For example, if you are in a cell containing a ~6~, you can jump to cell ~(2, 3)~.

Note that from a cell containing a ~6~, there are up to four cells you can jump to: ~(2, 3)~, ~(3, 2)~, ~(1, 6)~ or ~(6, 1)~. If the room is a ~5~-by-~6~ grid, there isn't a row ~6~ so only the first three jumps would be possible.

Input Specification

The first line of the input will be an integer ~M~ (~1 \le M \le 1000~). The second line of the input will be an integer ~N~ (~1 \le N \le 1000~). The remaining input gives the positive integers in the cells of the room with ~M~ rows and ~N~ columns. It consists of ~M~ lines where each line contains ~N~ positive integers, each less than or equal to ~10^6~, separated by single spaces.

For 1 of the 15 available marks, ~M = 2~ and ~N = 2~.

For an additional 2 of the 15 available marks, ~M = 1~.

For an additional 4 of the 15 available marks, all of the integers in the cells will be unique.

For an additional 4 of the 15 available marks, ~M \le 200~ and ~N \le 200~.

Output Specification

Output yes if it is possible to escape from the room. Otherwise, output no.

Sample Input

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

Sample Output

yes

Sample Explanation

Starting in the cell at ~(1, 1)~ which contains a ~3~, one possibility is to jump to the cell at ~(1, 3)~. This cell contains an ~8~ so from it, you could jump to the cell at ~(2, 4)~. This brings you to a cell containing ~12~ from which you can jump to the exit at ~(3, 4)~. Note that another way to escape is to jump from the starting cell to the cell at ~(3, 1)~ to the cell at ~(2, 3)~ to the exit.