Row Column Sums

AtCoder

IDarc133_c

Time2000ms

Memory256MB

Difficulty—

We have a grid with $H$ rows and $W$ columns. Snuke is going to write in each square an integer between $0$ and $K-1$ (inclusive). Here, the conditions below must be satisfied. * For each $1 \leq i \leq H$, the sum modulo $K$ of the integers written in the $i$\-th row is $A_i$. * For each $1 \leq i \leq W$, the sum modulo $K$ of the integers written in the $i$\-th column is $B_i$. Determine whether it is possible to write integers in the squares to satisfy the conditions. If it is possible, also find the maximum possible sum of the integers written. ## Constraints * $1 \leq H,W \leq 200000$ * $2 \leq K \leq 200000$ * $0 \leq A_i \leq K-1$ * $0 \leq B_i \leq K-1$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $H$ $W$ $K$ $A_1$ $A_2$ $\cdots$ $A_H$ $B_1$ $B_2$ $\cdots$ $B_W$ [samples]

Samples

Input #1

2 4 3
0 2
1 2 2 0

Output #1

11

The following should be written.

\-----------------
| 2 | 0 | 2 | 2 |
-----------------
| 2 | 2 | 0 | 1 |
-----------------

We can see that the conditions are satisfied. For example, the sum of the integers in the $1$\-st row is $6$, which modulo $K(=3)$ is $A_1(=0)$.
The sum of the integers written here is $11$, which is the maximum possible value.

Input #2

3 3 4
0 1 2
1 2 3

Output #2

\-1

API Response (JSON)

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    "name": "Row Column Sums",
    "description": {
      "content": "We have a grid with $H$ rows and $W$ columns. Snuke is going to write in each square an integer between $0$ and $K-1$ (inclusive). Here, the conditions below must be satisfied. *   For each $1 \\leq i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc133_c"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a grid with $H$ rows and $W$ columns.\nSnuke is going to write in each square an integer between $0$ and $K-1$ (inclusive). Here, the conditions below must be satisfied.\n\n*   For each $1 \\leq i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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