Contest Duration: - (local time) (100 minutes) Back to Home
E - Unfair Sugoroku /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

このとき xz \equiv y \pmod {998244353} を満たすような 0 以上 998244352 以下の整数 z が一意に定まります。この z を答えてください。

### 制約

• 2 \leq N \leq 100
• 1 \leq A, B < N
• 1 \leq P, Q \leq 10
• 入力はすべて整数

### 入力

N A B P Q


### 入力例 1

4 2 3 3 2


### 出力例 1

665496236


よって、高橋君が勝つ確率は \frac{2}{3} です。

### 入力例 2

6 4 2 1 1


### 出力例 2

1


サイコロの出目は常に 1 です。
このとき高橋君が地点 5 に進み、次いで青木君が地点 3 に進み、次いで高橋君が地点 6 に進むので、高橋君は必ず勝ちます。

### 入力例 3

100 1 1 10 10


### 出力例 3

264077814


Score : 500 points

### Problem Statement

Takahashi and Aoki will play a game of sugoroku.
Takahashi starts at point A, and Aoki starts at point B. They will take turns throwing dice.
Takahashi's die shows 1, 2, \ldots, P with equal probability, and Aoki's shows 1, 2, \ldots, Q with equal probability.
When a player at point x throws his die and it shows i, he goes to point \min(x + i, N).
The first player to reach point N wins the game.
Find the probability that Takahashi wins if he goes first, modulo 998244353.

How to find a probability modulo 998244353 It can be proved that the sought probability is always rational. Additionally, the constraints of this problem guarantee that, if that probability is represented as an irreducible fraction \frac{y}{x}, then x is indivisible by 998244353.
Here, there is a unique integer z between 0 and 998244352 such that xz \equiv y \pmod {998244353}. Report this z.

### Constraints

• 2 \leq N \leq 100
• 1 \leq A, B < N
• 1 \leq P, Q \leq 10
• All values in the input are integers.

### Input

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

N A B P Q


### Sample Input 1

4 2 3 3 2


### Sample Output 1

665496236


If Takahashi's die shows 2 or 3 in his first turn, he goes to point 4 and wins.
If Takahashi's die shows 1 in his first turn, he goes to point 3, and Aoki will always go to point 4 in the next turn and win.
Thus, Takahashi wins with the probability \frac{2}{3}.

### Sample Input 2

6 4 2 1 1


### Sample Output 2

1


The dice always show 1.
Here, Takahashi goes to point 5, Aoki goes to point 3, and Takahashi goes to point 6, so Takahashi always wins.

### Sample Input 3

100 1 1 10 10


### Sample Output 3

264077814