Alice is playing a game on an by grid of integers she got for Christmas, which she calls . 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 in that row. must have value at least . First, she subtracts one from . Then, she looks for the first zero to the right of , and adds one to that cell. If no such cell exists, she does no increment, but is still decremented. Columns are the same, and proceed top-down.

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

#### Constraints

##### Subtask 1 [20%]

##### Subtask 2 [80%]

No additional constraints.

#### Input Specification

The first line contains space-separated integers and .

The next lines contain space-separated integers representing grid .

The last lines contain space-separated integers representing grid .

#### Output Specification

Output `YES`

if 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`

## Comments