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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.

Sample Input 1

2 2 2

Sample Output 1

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.

Sample Input 2

1 1 100

Sample Output 2

100

Sample Input 3

31415 92653 58979

Sample Output 3

469486242