{"problem":{"name":"Ex - Typical Convolution Problem","description":{"content":"You are given a sequence $(A_1, A_2, \\ldots , A_N)$. Let us define a sequence $(F_0, F_1, \\ldots , F_N)$ by the following formulae. *   $F_0 = 1$ *   $F_n = A_n\\displaystyle\\sum_{i+j<n}F_iF_j$ $(1 \\l","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":5000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc315_h"},"statements":[{"statement_type":"Markdown","content":"You are given a sequence $(A_1, A_2, \\ldots , A_N)$. Let us define a sequence $(F_0, F_1, \\ldots , F_N)$ by the following formulae.\n\n*   $F_0 = 1$\n*   $F_n = A_n\\displaystyle\\sum_{i+j<n}F_iF_j$ $(1 \\leq n \\leq N)$\n\nFind $F_1, \\ldots , F_N$ modulo $998244353$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $0 \\leq A_i < 998244353$\n*   All input values are integers.\n\n## Input\n\nThe input 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":"abc315_h","tags":[],"sample_group":[["5\n1 2 3 4 5","1 6 48 496 6240\n\n$F_1 = A_1F_0F_0 = 1$. $F_2 = A_2(F_0F_0+F_0F_1+F_1F_0) = 6$. Similarly, we find $F_3 = 48, F_4 = 496, F_5 = 6240$."],["3\n12345 678901 2345678","12345 790834943 85679169"]],"created_at":"2026-03-03 11:01:14"}}