{"problem":{"name":"AtCoder Language","description":{"content":"The AtCoder language has $L$ different characters. How many $N$\\-character strings $s$ consisting of characters in the AtCoder language satisfy the following condition? Find the count modulo $99824435","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc172_b"},"statements":[{"statement_type":"Markdown","content":"The AtCoder language has $L$ different characters. How many $N$\\-character strings $s$ consisting of characters in the AtCoder language satisfy the following condition? Find the count modulo $998244353$.\n\n*   All $K$\\-character subsequences of the string $s$ are different. More precisely, there are $_N\\mathrm{C}_K$ ways to obtain a $K$\\-character string by extracting $K$ characters from the string $s$ and concatenating them without changing the order, and all of these ways must generate different strings.\n\nWhat is $_N\\mathrm{C}_K$?$_N\\mathrm{C}_K$ refers to the total number of ways to choose $K$ from $N$ items. More precisely, $_N\\mathrm{C}_K$ is the value of $N!$ divided by $K! \\times (N-K)!$.\n\n## Constraints\n\n*   $1 \\leq K < N \\leq 500000$\n*   $1 \\leq L \\leq 10^9$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $K$ $L$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc172_b","tags":[],"sample_group":[["4 3 2","2\n\nIf `a` and `b` represent the first and second characters in the language, the condition is satisfied by two strings: `abab` and `baba`."],["100 80 26","496798269\n\nApproximately $10^{86}$ strings satisfy the condition, but here we print the count modulo $998244353$, which is $496798269$."],["100 1 26","0"],["500000 172172 503746693","869120"]],"created_at":"2026-03-03 11:01:14"}}