{"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"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc154_f"},"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 follows:\n\n*   $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)\n\nGiven 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 $(10^9+7)$.\n\n## Constraints\n\n*   $1 ≤ r_1 ≤ r_2 ≤ 10^6$\n*   $1 ≤ c_1 ≤ c_2 ≤ 10^6$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$r_1$ $c_1$ $r_2$ $c_2$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc154_f","tags":[],"sample_group":[["1 1 2 2","14\n\nFor 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 $f(1,1)=2$.\nSimilarly, $f(1,2)=3$, $f(2,1)=3$, and $f(2,2)=6$. Thus, the sum is $14$."],["314 159 2653 589","602215194"]],"created_at":"2026-03-03 11:01:13"}}