Problem Statement

There is $a H \times W-square$ grid with H horizontal rows and W vertical columns. Let (i, j) denote the square at the i-th row from the top and j-th column from the left.
The grid has a rook, initially on (x_1, y_1). Takahashi will do the following operation K times.

• Move the rook to a square that shares the row or column with the square currently occupied by the rook. Here, it must move to a square different from the current one.

How many ways are there to do the K operations so that the rook will be on (x_2, y_2) in the end? Since the answer can be enormous, find it modulo 998244353.

Input

Input is given from Standard Input in the following format:
H W K
x_1 y_1 x_2 y_2

Output

Print the number of ways to do the K operations so that the rook will be on (x_2, y_2) in the end, modulo 998244353.

Constraints

• $2 \leq H, W \leq 10^9$
• $1 \leq K \leq 10^6$
• $1 \leq x_1, x_2 \leq H$
• $1 \leq y_1, y_2 \leq W$

Sample Input 1

2 2 2
1 2 2 1

Sample Output 1

2

We have the following two ways.

• First, move the rook from (1, 2) to (1, 1). Second, move it from (1, 1) to (2, 1).
• First, move the rook from (1, 2) to (2, 2). Second, move it from (2, 2) to (2, 1).

Sample Input 2

1000000000 1000000000 1000000
1000000000 1000000000 1000000000 1000000000

Sample Output 2

24922282

Be sure to find the count modulo 998244353.

Sample Input 3

3 3 3
1 3 3 3

Sample Output 3

9

见题面 Input 部分

见题面 Output 部分