{"problem":{"name":"Sky Reflector","description":{"content":"In a grid with $N$ horizontal rows and $M$ vertical columns of squares, we will write an integer between $1$ and $K$ (inclusive) on each square and define sequences $A, B$ as follows: *   for each $i","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc113_d"},"statements":[{"statement_type":"Markdown","content":"In a grid with $N$ horizontal rows and $M$ vertical columns of squares, we will write an integer between $1$ and $K$ (inclusive) on each square and define sequences $A, B$ as follows:\n\n*   for each $i=1,\\dots, N$, $A_i$ is the minimum value written on a square in the $i$\\-th row;\n*   for each $j=1,\\dots, M$, $B_j$ is the maximum value written on a square in the $j$\\-th column.\n\nGiven $N, M, K$, find the number of different pairs of sequences that can be $(A, B)$, modulo $998244353$.\n\n## Constraints\n\n*   $1 \\leq N,M,K \\leq 2\\times 10^5$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$ $K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc113_d","tags":[],"sample_group":[["2 2 2","7\n\n$(A_1,A_2,B_1,B_2)$ can be $(1,1,1,1)$, $(1,1,1,2)$, $(1,1,2,1)$, $(1,1,2,2)$, $(1,2,2,2)$, $(2,1,2,2)$, or $(2,2,2,2)$ - there are seven candidates."],["1 1 100","100"],["31415 92653 58979","469486242"]],"created_at":"2026-03-03 11:01:14"}}