Score : $600$ points

Problem Statement

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 $i=1,\dots, N$, $A_i$ is the minimum value written on a square in the $i$-th row;
• for each $j=1,\dots, M$, $B_j$ is the maximum value written on a square in the $j$-th column.

Given $N, M, K$, find the number of different pairs of sequences that can be $(A, B)$, modulo $998244353$.

Constraints

• $1 \leq N,M,K \leq 2\times 10^5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $K$

Output

Print the number of different pairs of sequences that can be $(A, B)$, modulo $998244353$.

2 2 2

7

$(A_1,A_2,B_1,B_2)$ 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