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