9801: ABC264 —— C - Matrix Reducing
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Description
You are given a matrix $A$ with $H_1$ rows and $W_1$ columns, and a matrix $B$ with $H_2$ rows and $W_2$ columns.
- For all integer pairs $(i, j)$ such that $1 \leq i \leq H_1$ and $1 \leq j \leq W_1$, the element at the $i$-th row and $j$-th column of matrix $A$ is $A_{i, j}$.
- For all integer pairs $(i, j)$ such that $1 \leq i \leq H_2$ and $1 \leq j \leq W_2$, the element at the $i$-th row and $j$-th column of matrix $B$ is $B_{i, j}$.
You may perform the following operations on the matrix $A$ any number of (possibly $0$) times in any order:
- Choose an arbitrary row of $A$ and remove it.
- Choose an arbitrary column of $A$ and remove it.
Determine if it is possible to make the matrix $A$ equal the matrix $B$.
- For all integer pairs $(i, j)$ such that $1 \leq i \leq H_1$ and $1 \leq j \leq W_1$, the element at the $i$-th row and $j$-th column of matrix $A$ is $A_{i, j}$.
- For all integer pairs $(i, j)$ such that $1 \leq i \leq H_2$ and $1 \leq j \leq W_2$, the element at the $i$-th row and $j$-th column of matrix $B$ is $B_{i, j}$.
You may perform the following operations on the matrix $A$ any number of (possibly $0$) times in any order:
- Choose an arbitrary row of $A$ and remove it.
- Choose an arbitrary column of $A$ and remove it.
Determine if it is possible to make the matrix $A$ equal the matrix $B$.
Input
Input is given from Standard Input in the following format:
```
$H_1$ $W_1$
$A_{1, 1}$ $A_{1, 2}$ $\ldots$ $A_{1, W_1}$
$A_{2, 1}$ $A_{2, 2}$ $\ldots$ $A_{2, W_1}$
$\vdots$
$A_{H_1, 1}$ $A_{H_1, 2}$ $\ldots$ $A_{H_1, W_1}$
$H_2$ $W_2$
$B_{1, 1}$ $B_{1, 2}$ $\ldots$ $B_{1, W_2}$
$B_{2, 1}$ $B_{2, 2}$ $\ldots$ $B_{2, W_2}$
$\vdots$
$B_{H_2, 1}$ $B_{H_2, 2}$ $\ldots$ $B_{H_2, W_2}$
```
```
$H_1$ $W_1$
$A_{1, 1}$ $A_{1, 2}$ $\ldots$ $A_{1, W_1}$
$A_{2, 1}$ $A_{2, 2}$ $\ldots$ $A_{2, W_1}$
$\vdots$
$A_{H_1, 1}$ $A_{H_1, 2}$ $\ldots$ $A_{H_1, W_1}$
$H_2$ $W_2$
$B_{1, 1}$ $B_{1, 2}$ $\ldots$ $B_{1, W_2}$
$B_{2, 1}$ $B_{2, 2}$ $\ldots$ $B_{2, W_2}$
$\vdots$
$B_{H_2, 1}$ $B_{H_2, 2}$ $\ldots$ $B_{H_2, W_2}$
```
Output
Print `Yes` if it is possible to make the matrix $A$ equal the matrix $B$; print `No` otherwise. Note that the judge is case-sensitive.
Constraints
- $1 \leq H_2 \leq H_1 \leq 10$
- $1 \leq W_2 \leq W_1 \leq 10$
- $1 \leq A_{i, j} \leq 10^9$
- $1 \leq B_{i, j} \leq 10^9$
- All values in input are integers.
- $1 \leq W_2 \leq W_1 \leq 10$
- $1 \leq A_{i, j} \leq 10^9$
- $1 \leq B_{i, j} \leq 10^9$
- All values in input are integers.
Sample 1 Input
4 5
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
2 3
6 8 9
16 18 19
Sample 1 Output
Yes
Removing the 2-nd column from the initial A results in:
1 3 4 5 6 8 9 10 11 13 14 15 16 18 19 20
Then, removing the 3-rd row from A results in:
1 3 4 5 6 8 9 10 16 18 19 20
Then, removing the 1-st row from A results in:
6 8 9 10 16 18 19 20
Then, removing the 4-th column from A results in:
6 8 9 16 18 19
Now the matrix equals the matrix B.
Thus, we can make the matrix A equal the matrix B by repeating the operations, so Yes should be printed.
Sample 2 Input
3 3
1 1 1
1 1 1
1 1 1
1 1
2
Sample 2 Output
No