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.

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.

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

见题面 Input 部分

见题面 Output 部分