{"raw_statement":[{"iden":"problem statement","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 $998244353$."},{"iden":"constraints","content":"*   $1 \\leq N,M,K \\leq 2\\times 10^5$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$ $K$"},{"iden":"sample input 1","content":"2 2 2"},{"iden":"sample output 1","content":"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."},{"iden":"sample input 2","content":"1 1 100"},{"iden":"sample output 2","content":"100"},{"iden":"sample input 3","content":"31415 92653 58979"},{"iden":"sample output 3","content":"469486242"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}