{"problem":{"name":"Sequence Sum","description":{"content":"Let us denote by $f(x, m)$ the remainder of the Euclidean division of $x$ by $m$. Let $A$ be the sequence that is defined by the initial value $A_1=X$ and the recurrence relation $A_{n+1} = f(A_n^2, M","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc179_e"},"statements":[{"statement_type":"Markdown","content":"Let us denote by $f(x, m)$ the remainder of the Euclidean division of $x$ by $m$.\nLet $A$ be the sequence that is defined by the initial value $A_1=X$ and the recurrence relation $A_{n+1} = f(A_n^2, M)$. Find $\\displaystyle{\\sum_{i=1}^N A_i}$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^{10}$\n*   $0 \\leq X < M \\leq 10^5$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $X$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc179_e","tags":[],"sample_group":[["6 2 1001","1369\n\nThe sequence $A$ begins $2,4,16,256,471,620,\\ldots$ Therefore, the answer is $2+4+16+256+471+620=1369$."],["1000 2 16","6\n\nThe sequence $A$ begins $2,4,0,0,\\ldots$ Therefore, the answer is $6$."],["10000000000 10 99959","492443256176507"]],"created_at":"2026-03-03 11:01:14"}}