Problem Statement

There is a city consisting of $\ HW\ $ blocks in total, divided into a grid with $\ H\ $ rows and $\ W\ $ columns.

Let $\ (i,j)\ $ denote the block in the $\ i\ $-th row from the top and the $\ j\ $-th column from the left. For two blocks $\ A,B\ $, the distance between the two blocks is defined as follows.

• When block $\ A\ $ is $\ (p,q)\ $ and block $\ B\ $ is $\ (r,s)\ $, the distance between blocks $\ A\ $ and $\ B\ $ is $\ |p-r|+|q-s|$

Now Mitsubachi-kun and Mitarushi-kun are both at $\ (1,1)\ $. They head for $\ (H,W)\ $ by repeatedly choosing the block adjacent below or to the right and moving there, simultaneously and at the same speed. (The two may choose different directions of movement.)
How many pairs of movement paths of the two are there such that the distance between the two blocks they are on is always at most $\ K\ $?

Since the answer can be very large, find it modulo $\ 998244353\ $.

Here, two pairs of movement paths of the two are considered different when the following holds.

• There exists an integer $\ i\ $ such that, for the $\ i\ $-th block of the movement paths, it is not the case that "the block where Mitsubachi-kun is located is the same and the block where Mitarushi-kun is located is the same"

Input

$H\ W\ K$

• $ 2 \leq H,W \leq 2 \times 10^5$
• $ 0 \leq K \leq H+W-2$
• All inputs are integers

Output

Output the number of possible pairs of movement paths of the two, modulo $\ 998244353\ $.
Print a newline at the end.

Sample

3 3 2

34

ミツバチ君:$\ (1,1) \rightarrow (1,2) \rightarrow (2,2) \rightarrow (3,2) \rightarrow (3,3)$
ミタルシ君:$\ (1,1) \rightarrow (2,1) \rightarrow (3,1) \rightarrow (3,2) \rightarrow (3,3)$

$0 \rightarrow 2 \rightarrow 2 \rightarrow 0 \rightarrow 0$

10 10 0

48620

314 1592 653

13839116