Problem Statement

There is a shogi (Japanese chess) board with $H$ rows and $W$ columns, and one king piece. The square at the $i$-th row from the top and $j$-th column from the left of the board is represented as $(i, j)$. Initially, the king is placed at $(A, B)$. You perform the following operation exactly $T$ times.

• Move the king to one of the eight adjacent squares of the current square. More precisely, if the king is at square $(i, j)$, move the king to one of $(i+1,j+1), (i+1,j), (i+1,j-1), (i,j+1), (i,j-1), (i-1,j+1), (i-1,j), (i-1,j-1)$. The king cannot leave the board.

Find the number, modulo $998244353$, of operation sequences such that the king is at $(C, D)$ after completing all $T$ operations. Two operation sequences are considered different if and only if there exists an integer $i$ $(1 \leq i \leq T)$ such that the king's position after the $i$-th operation is different.

Constraints

• $2 \leq H \leq 3 \times 10^5$
• $2 \leq W \leq 3 \times 10^5$
• $1 \leq T \leq 3 \times 10^5$
• $1 \leq A \leq H$
• $1 \leq B \leq W$
• $1 \leq C \leq H$
• $1 \leq D \leq W$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

H W T A B C D

Output

Output the number, modulo $998244353$, of operation sequences such that the king is at $(C, D)$ after completing all $T$ operations.