{"problem":{"name":"Integer Sequence Fair","description":{"content":"Integer Sequence Exhibition is taking place, where integer sequences are gathered in one place and evaluated. Here, every integer sequence of length $N$ consisting of integers between $1$ and $K$ (inc","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc228_e"},"statements":[{"statement_type":"Markdown","content":"Integer Sequence Exhibition is taking place, where integer sequences are gathered in one place and evaluated. Here, every integer sequence of length $N$ consisting of integers between $1$ and $K$ (inclusive) is evaluated and given an integer score between $1$ and $M$ (inclusive).\nPrint the number, modulo $998244353$, of ways to give each of the evaluated sequences a score between $1$ and $M$.\nHere, two ways are said to be different when there is an evaluated sequence $A = (A_1, A_2, \\ldots, A_N)$ that is given different scores by the two ways.\n\n## Constraints\n\n*   $1 \\leq N, K, M \\leq 10^{18}$\n*   $N$, $K$, and $M$ are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc228_e","tags":[],"sample_group":[["2 2 2","16\n\nFour sequences are evaluated: $(1, 1)$, $(1, 2)$, $(2, 1)$, and $(2, 2)$. There are $16$ ways to give each of these sequences a score between $1$ and $2$, as follows.\n\n*   Give $1$ to $(1, 1)$, $1$ to $(1, 2)$, $1$ to $(2, 1)$, and $1$ to $(2, 2)$\n*   Give $1$ to $(1, 1)$, $1$ to $(1, 2)$, $1$ to $(2, 1)$, and $2$ to $(2, 2)$\n*   Give $1$ to $(1, 1)$, $1$ to $(1, 2)$, $2$ to $(2, 1)$, and $1$ to $(2, 2)$\n*   Give $1$ to $(1, 1)$, $1$ to $(1, 2)$, $2$ to $(2, 1)$, and $2$ to $(2, 2)$\n*   $\\cdots$\n*   Give $2$ to $(1, 1)$, $2$ to $(1, 2)$, $2$ to $(2, 1)$, and $2$ to $(2, 2)$\n\nThus, we print $16$."],["3 14 15926535","109718301\n\nBe sure to print the count modulo $998244353$."]],"created_at":"2026-03-03 11:01:14"}}