408063: GYM102978 A Ascending Matrix

You are given integers $$$N,M,K,R,C,$$$ and $$$V$$$. Find the number of $$$N$$$ by $$$M$$$ integer matrices $$$a = (a_{i,j})$$$ that satisfy all of the following conditions, modulo $$$998244353$$$.

• $$$1 \leq a_{i,j} \leq K$$$ for all $$$1 \leq i \leq N,\, 1 \leq j \leq M$$$.
• $$$a_{i,j} \leq a_{i,j+1}$$$ for all $$$1 \leq i \leq N,\, 1 \leq j \leq M-1$$$.
• $$$a_{i,j} \leq a_{i+1,j}$$$ for all $$$1 \leq i \leq N-1,\, 1 \leq j \leq M$$$.
• $$$a_{R,C}=V$$$.

The first line contains integers $$$N$$$, $$$M$$$ ($$$1 \leq N,M \leq 200$$$), $$$K$$$ ($$$1 \leq K \leq 100$$$), $$$R$$$ ($$$1 \leq R \leq N$$$), $$$C$$$ ($$$1 \leq C \leq M$$$), and $$$V$$$ ($$$1 \leq V \leq K$$$).

Print the answer.

2 2 2 1 1 1

5

2 2 2 1 2 1

3

4 5 6 2 3 4

3700125

200 100 100 70 60 30

546626227