{"problem":{"name":"[语言月赛 202401] 区间函数最大值","description":{"content":"给定 $A, B, C, D, E, F, G, P, X_1, X_2, Y_1, Y_2$，求当 $X _ 1 \\leq x \\leq X _ 2$，$Y _ 1 \\leq y \\leq Y _ 2$ 且 $x, y$ 均为整数时 $$ f(x, y) = (A x ^ 3 + B y ^ 3 + C x ^ 2 y + Dxy ^ 2 + Exy + Fx + Gy) \\bmod P $$","description_type":"Markdown"},"platform":"Luogu","limit":{"time_limit":1000,"memory_limit":524288},"difficulty":{"LuoguStyle":"P1"},"is_remote":true,"is_sync":true,"sync_url":null,"sign":"LGB3916"},"statements":[{"statement_type":"Markdown","content":"给定 $A, B, C, D, E, F, G, P, X_1, X_2, Y_1, Y_2$，求当 $X _ 1 \\leq x \\leq X _ 2$，$Y _ 1 \\leq y \\leq Y _ 2$ 且 $x, y$ 均为整数时\n\n$$\nf(x, y) = (A x ^ 3 + B y ^ 3 + C x ^ 2 y + Dxy ^ 2 + Exy + Fx + Gy) \\bmod P\n$$\n\n的最大值。\n\n$x \\bmod K$ 代表 $x$ 除以 $K$ 的余数，例如 $7 \\bmod 3 = 1$。\n\n## Input\n\n输入共一行十二个整数 $A, B, C, D, E, F, G, P, X_1, X_2, Y_1, Y_2$。\n\n## Output\n\n输出一个整数，代表 $f(x, y)$ 的最大值。\n\n[samples]\n\n## Note\n\n### 样例解释 #1\n\n当 $x$ 为 $1$ 或 $2$，$y$ 为 $1$ 到 $3$ 之间的整数时，函数 $f(x,y)$ 的值如下：\n\n$$\nf(1,1)=23,\\ f(1,2)=63,\\ f(1,3)=139\\\\\nf(2,1)=70,\\ f(2,2)=144,\\ f(2,3)=266\n$$\n\n最大值为 $f(2,3)$，即 $266$。\n\n### 数据规模与约定\n\n对于 $100\\%$ 的数据，保证 $1 \\leq A, B, C, D, E, F, G, P \\leq 10 ^ 9$，$1 \\leq X _ 1 \\leq X _ 2 \\leq 10 ^ 3$，$1 \\leq Y _ 1 \\leq Y _ 2 \\leq 10 ^ 3$。","is_translate":false,"language":"English"}],"meta":{"iden":"LGB3916","tags":["2024","O2优化","循环结构","语言月赛"],"sample_group":[["3 2 5 6 1 4 2 998244353 1 2 1 3\n","266\n"]],"created_at":"2026-03-03 11:09:25"}}