{"problem":{"name":"Mod i","description":{"content":"Given is a sequence $A$ of $N$ numbers. Find the number of ways to separate $A$ into some number of non-empty contiguous subsequence $B_1, B_2, \\ldots, B_k$ so that the following condition is satisfie","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc207_e"},"statements":[{"statement_type":"Markdown","content":"Given is a sequence $A$ of $N$ numbers. Find the number of ways to separate $A$ into some number of non-empty contiguous subsequence $B_1, B_2, \\ldots, B_k$ so that the following condition is satisfied:\n\n*   For every $i\\ (1 \\leq i \\leq k)$, the sum of elements in $B_i$ is divisible by $i$.\n\nSince the count can be enormous, print it modulo $(10^9+7)$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 3000$\n*   $1 \\leq A_i \\leq 10^{15}$\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$A_1$ $A_2$ $\\ldots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc207_e","tags":[],"sample_group":[["4\n1 2 3 4","3\n\nWe have three ways to separate the sequence, as follows:\n\n*   $(1),(2),(3),(4)$\n*   $(1,2,3),(4)$\n*   $(1,2,3,4)$"],["5\n8 6 3 3 3","5"],["10\n791754273866483 706434917156797 714489398264550 918142301070506 559125109706263 694445720452148 648739025948445 869006293795825 718343486637033 934236559762733","15\n\nThe values in input may not fit into a $32$\\-bit integer type."]],"created_at":"2026-03-03 11:01:14"}}