Matrix Reducing

AtCoder

IDabc264_c

Time2000ms

Memory256MB

Difficulty—

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 $B$. ## 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. ## Input Input is given from Standard Input in the following format: $H_1$ $W_1$ $A_{1, 1}$ $A_{1, 2}$ $\ldots$ $A_{1, W_1}$ $A_{2, 1}$ $A_{2, 2}$ $\ldots$ $A_{2, W_1}$ $\vdots$ $A_{H_1, 1}$ $A_{H_1, 2}$ $\ldots$ $A_{H_1, W_1}$ $H_2$ $W_2$ $B_{1, 1}$ $B_{1, 2}$ $\ldots$ $B_{1, W_2}$ $B_{2, 1}$ $B_{2, 2}$ $\ldots$ $B_{2, W_2}$ $\vdots$ $B_{H_2, 1}$ $B_{H_2, 2}$ $\ldots$ $B_{H_2, W_2}$ [samples]

Samples

Input #1

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

Output #1

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.

Input #2

Output #2

No

Regardless of how we perform the operations, we cannot make the matrix $A$ equal the matrix $B$, so `No` should be printed.

API Response (JSON)

{
  "problem": {
    "name": "Matrix Reducing",
    "description": {
      "content": "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",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc264_c"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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.\n\n*   For all integer pairs $(i, j)$ such that $1 \\leq i \\leq H_1$ and $1 \\leq j \\leq W...",
      "is_translate": false,
      "language": "English"
    }
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}

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