{"problem":{"name":"Fusing Slimes","description":{"content":"There are $N$ slimes standing on a number line. The $i$\\-th slime from the left is at position $x_i$. It is guaruanteed that $1 \\leq x_1 < x_2 < \\ldots < x_N \\leq 10^{9}$. Niwango will perform $N-1$ o","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2525,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"dwacon6th_prelims_b"},"statements":[{"statement_type":"Markdown","content":"There are $N$ slimes standing on a number line. The $i$\\-th slime from the left is at position $x_i$.\nIt is guaruanteed that $1 \\leq x_1 < x_2 < \\ldots < x_N \\leq 10^{9}$.\nNiwango will perform $N-1$ operations. The $i$\\-th operation consists of the following procedures:\n\n*   Choose an integer $k$ between $1$ and $N-i$ (inclusive) with equal probability.\n*   Move the $k$\\-th slime from the left, to the position of the neighboring slime to the right.\n*   Fuse the two slimes at the same position into one slime.\n\nFind the total distance traveled by the slimes multiplied by $(N-1)!$ (we can show that this value is an integer), modulo $(10^{9}+7)$. If a slime is born by a fuse and that slime moves, we count it as just one slime.\n\n## Constraints\n\n*   $2 \\leq N \\leq 10^{5}$\n*   $1 \\leq x_1 < x_2 < \\ldots < x_N \\leq 10^{9}$\n*   $x_i$ is an integer.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$x_1$ $x_2$ $\\ldots$ $x_N$\n\n## Subtasks\n\n*   $400$ points will be awarded for passing the test cases satisfying $N \\leq 2000$.\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"dwacon6th_prelims_b","tags":[],"sample_group":[["3\n1 2 3","5\n\n*   With probability $\\frac{1}{2}$, the leftmost slime is chosen in the first operation, in which case the total distance traveled is $2$.\n*   With probability $\\frac{1}{2}$, the middle slime is chosen in the first operation, in which case the total distance traveled is $3$.\n*   The answer is the expected total distance traveled, $2.5$, multiplied by $2!$, which is $5$."],["12\n161735902 211047202 430302156 450968417 628894325 707723857 731963982 822804784 880895728 923078537 971407775 982631932","750927044\n\n*   Find the expected value multiplied by $(N-1)!$, modulo $(10^9+7)$."]],"created_at":"2026-03-03 11:01:14"}}