Alice is playing a game on an ~N~ by ~M~ grid of integers she got for Christmas, which she calls ~A~. In one move, she can rebalance a row or column. A rebalancing is an operation performed on a row or column. The operation will be described on rows. First, Alice picks a row, and then she picks a cell ~C~ in that row. ~C~ must have value at least ~1~. First, she subtracts one from ~C~. Then, she looks for the first zero to the right of ~C~, and adds one to that cell. If no such cell exists, she does no increment, but ~C~ is still decremented. Columns are the same, and proceed top-down.

Alice really likes the grid ~B~, because Bob got it for Christmas and she is jealous. Please tell Alice if it is possible to achieve ~B~ after some amount of rebalancings.

Constraints

~1 \le N, M \le 100~

~0 \le A_i, B_i \le 10^9~

Subtask 1 [20%]

~N = 1~

Subtask 2 [80%]

No additional constraints.

Input Specification

The first line contains ~2~ space-separated integers ~N~ and ~M~.

The next ~N~ lines contain ~M~ space-separated integers ~A_{i,j}~ representing grid ~A~.

The last ~N~ lines contain ~M~ space-separated integers ~B_{i,j}~ representing grid ~B~.

Output Specification

Output YES if ~B~ can be achieved after some amount of rebalancings, and NO otherwise.

Sample Input

2 3
2 2 0
0 0 0
0 0 1
0 1 1

Sample Output

YES