###

AtCoder

IDarc071_b

Time2000ms

Memory256MB

Difficulty—

On a two-dimensional plane, there are $m$ lines drawn parallel to the $x$ axis, and $n$ lines drawn parallel to the $y$ axis. Among the lines parallel to the $x$ axis, the $i$\-th from the bottom is represented by $y = y_i$. Similarly, among the lines parallel to the $y$ axis, the $i$\-th from the left is represented by $x = x_i$. For every rectangle that is formed by these lines, find its area, and print the total area modulo $10^9+7$. That is, for every quadruple $(i,j,k,l)$ satisfying $1\leq i < j\leq n$ and $1\leq k < l\leq m$, find the area of the rectangle formed by the lines $x=x_i$, $x=x_j$, $y=y_k$ and $y=y_l$, and print the sum of these areas modulo $10^9+7$. ## Constraints * $2 \leq n,m \leq 10^5$ * $-10^9 \leq x_1 < ... < x_n \leq 10^9$ * $-10^9 \leq y_1 < ... < y_m \leq 10^9$ * $x_i$ and $y_i$ are integers. ## Input Input is given from Standard Input in the following format: $n$ $m$ $x_1$ $x_2$ $...$ $x_n$ $y_1$ $y_2$ $...$ $y_m$ [samples]

Samples

Input #1

3 3
1 3 4
1 3 6

Output #1

60

The following figure illustrates this input:
![image](https://atcoder.jp/img/arc071/aec4d5cc2e5c73dbee455be237a649a5.png)
The total area of the nine rectangles A, B, ..., I shown in the following figure, is $60$.
![image](https://atcoder.jp/img/arc071/f0771c0f7e68af2b00e7513186f585ff.png)

Input #2

6 5
-790013317 -192321079 95834122 418379342 586260100 802780784
-253230108 193944314 363756450 712662868 735867677

Output #2

835067060

API Response (JSON)

{
  "problem": {
    "name": "###",
    "description": {
      "content": "On a two-dimensional plane, there are $m$ lines drawn parallel to the $x$ axis, and $n$ lines drawn parallel to the $y$ axis. Among the lines parallel to the $x$ axis, the $i$\\-th from the bottom is r",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc071_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "On a two-dimensional plane, there are $m$ lines drawn parallel to the $x$ axis, and $n$ lines drawn parallel to the $y$ axis. Among the lines parallel to the $x$ axis, the $i$\\-th from the bottom is r...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments