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,\dots,M~ and the columns are numbered ~1,2,\dots,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 1\,000)~. The second line of the input will be an integer ~N~ ~(1 \le N \le 1\,000)~. 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 ~1\,000\,000~, 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

Output for Sample Input

yes

Explanation of Output for Sample Input

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.

Notes

1. The online grader begins by testing submissions using the sample input. All other tests are skipped if the sample test is not passed. If you are only attempting the first three subtasks (the first ~7~ marks), then you might want to handle the specific values of the sample input as a special case.

2. For the final subtask (worth ~2~ marks), if you are using Java, then Scanner will probably take too long to read in the large amount of data. A much faster alternative is BufferedReader.