Many Many Paths

AtCoder

IDabc154_f

Time2000ms

Memory256MB

Difficulty—

Snuke is standing on a two-dimensional plane. In one operation, he can move by $1$ in the positive $x$\-direction, or move by $1$ in the positive $y$\-direction. Let us define a function $f(r, c)$ as follows: * $f(r,c) := $ (The number of paths from the point $(0, 0)$ to the point $(r, c)$ that Snuke can trace by repeating the operation above) Given are integers $r_1$, $r_2$, $c_1$, and $c_2$. Find the sum of $f(i, j)$ over all pair of integers $(i, j)$ such that $r_1 ≤ i ≤ r_2$ and $c_1 ≤ j ≤ c_2$, and compute this value modulo $(10^9+7)$. ## Constraints * $1 ≤ r_1 ≤ r_2 ≤ 10^6$ * $1 ≤ c_1 ≤ c_2 ≤ 10^6$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $r_1$ $c_1$ $r_2$ $c_2$ [samples]

Samples

Input #1

1 1 2 2

Output #1

14

For example, there are two paths from the point $(0, 0)$ to the point $(1, 1)$: $(0,0)$ → $(0,1)$ → $(1,1)$ and $(0,0)$ → $(1,0)$ → $(1,1)$, so $f(1,1)=2$.
Similarly, $f(1,2)=3$, $f(2,1)=3$, and $f(2,2)=6$. Thus, the sum is $14$.

Input #2

314 159 2653 589

Output #2

602215194

API Response (JSON)

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  "problem": {
    "name": "Many Many Paths",
    "description": {
      "content": "Snuke is standing on a two-dimensional plane. In one operation, he can move by $1$ in the positive $x$\\-direction, or move by $1$ in the positive $y$\\-direction. Let us define a function $f(r, c)$ as ",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc154_f"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke is standing on a two-dimensional plane. In one operation, he can move by $1$ in the positive $x$\\-direction, or move by $1$ in the positive $y$\\-direction.\nLet us define a function $f(r, c)$ as ...",
      "is_translate": false,
      "language": "English"
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