{"problem":{"name":"Many Good Tuple Problems","description":{"content":"> The definition of a good pair of sequences in this problem is the same as in Problem D. A pair of sequences of length $M$ consisting of positive integers at most $N$, $(S, T) = ((S_1, S_2, \\dots, S","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc327_g"},"statements":[{"statement_type":"Markdown","content":"> The definition of a good pair of sequences in this problem is the same as in Problem D.\n\nA pair of sequences of length $M$ consisting of positive integers at most $N$, $(S, T) = ((S_1, S_2, \\dots, S_M), (T_1, T_2, \\dots, T_M))$, is said to **be a good pair of sequences** when $(S, T)$ satisfies the following condition.\n\n*   There exists a sequence $X = (X_1, X_2, \\dots, X_N)$ of length $N$ consisting of $0$ and $1$ that satisfies the following condition:\n    *   $X_{S_i} \\neq X_{T_i}$ for each $i=1, 2, \\dots, M$.\n\nAmong the $N^{2M}$ possible pairs of sequences of length $M$ consisting of positive integers at most $N$, $(A, B) = ((A_1, A_2, \\dots, A_M), (B_1, B_2, \\dots, B_M))$, find the number, modulo $998244353$, of those that are good pairs of sequences.\n\n## Constraints\n\n*   $1 \\leq N \\leq 30$\n*   $1 \\leq M \\leq 10^9$\n*   $N$ and $M$ are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc327_g","tags":[],"sample_group":[["3 2","36\n\nFor example, if $A=(1,2), B=(2,3)$, then $(A, B)$ is a good pair of sequences. Indeed, if we set $X=(0,1,0)$, then $X$ is a sequence of length $N$ consisting of $0$ and $1$ that satisfies $X_{A_1} \\neq X_{B_1}$ and $X_{A_2} \\neq X_{B_2}$. Thus, $(A, B)$ satisfies the condition of being a good pair of sequences.  \nThere are a total of $36$ good pairs of sequences, so print this number."],["3 3","168"],["12 34","539029838"],["20 231104","966200489"]],"created_at":"2026-03-03 11:01:14"}}