{"problem":{"name":"Distribution","description":{"content":"There are $N$ creatures standing in a circle, called Snuke $1, 2, ..., N$ in counter-clockwise order. When Snuke $i$ $(1 \\leq i \\leq N)$ receives a gem at time $t$, $S_i$ units of time later, it will ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc214_c"},"statements":[{"statement_type":"Markdown","content":"There are $N$ creatures standing in a circle, called Snuke $1, 2, ..., N$ in counter-clockwise order.\nWhen Snuke $i$ $(1 \\leq i \\leq N)$ receives a gem at time $t$, $S_i$ units of time later, it will hand that gem to Snuke $i+1$ at time $t+S_i$. Here, Snuke $N+1$ is Snuke $1$.\nAdditionally, Takahashi will hand a gem to Snuke $i$ at time $T_i$.\nFor each $i$ $(1 \\leq i \\leq N)$, find the time when Snuke $i$ receives a gem for the first time. Assume that it takes a negligible time to hand a gem.\n\n## Constraints\n\n*   $1 \\leq N \\leq 200000$\n*   $1 \\leq S_i,T_i \\leq 10^9$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$S_1$ $S_2$ $\\ldots$ $S_N$\n$T_1$ $T_2$ $\\ldots$ $T_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc214_c","tags":[],"sample_group":[["3\n4 1 5\n3 10 100","3\n7\n8\n\nWe will list the three Snuke's and Takahashi's actions up to time $13$ in chronological order.\nTime $3$: Takahashi hands a gem to Snuke $1$.\nTime $7$: Snuke $1$ hands a gem to Snuke $2$.\nTime $8$: Snuke $2$ hands a gem to Snuke $3$.\nTime $10$: Takahashi hands a gem to Snuke $2$.\nTime $11$: Snuke $2$ hands a gem to Snuke $3$.\nTime $13$: Snuke $3$ hands a gem to Snuke $1$.\nAfter that, they will continue handing gems, though it will be irrelevant to the answer."],["4\n100 100 100 100\n1 1 1 1","1\n1\n1\n1\n\nNote that the values $S_i$ and $T_i$ may not be distinct."],["4\n1 2 3 4\n1 2 4 7","1\n2\n4\n7\n\nNote that a Snuke may perform multiple transactions simultaneously. Particularly, a Snuke may receive gems simultaneously from Takahashi and another Snuke."],["8\n84 87 78 16 94 36 87 93\n50 22 63 28 91 60 64 27","50\n22\n63\n28\n44\n60\n64\n27"]],"created_at":"2026-03-03 11:01:13"}}