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문제

You are in charge of organizing the new edition of Arctic Competition for Monkeys (ACM). There are $n$ monkeys taking part in this competition. The monkeys are numbered from 1 to $n$. Every two monkeys participate in a separate contest with one problem against each other. There are no ties. Whenever $i < j$, monkey $i$ defeats monkey $j$ with fixed probability $p$.

You've been asked by your manager to calculate the entertainment coefficient of the competition. You have no idea what this coefficient means, neither does your manager, so you've decided to come up with a fairly weird definition.

Let $f(k)$ be the probability that there exists a set of exactly $k$ monkeys such that every monkey in this set defeats every monkey not in this set.

Let $g(k)$ be a pseudo-random sequence defined recursively as follows:

$g(1) = 1$;

$g(i + 1) = (g(i))^2 + 2$ (for $i \ge 2$).

Then you've defined the entertainment coefficient to be equal to the following value:

$\sum \limits_{k=1}^{n-1} f(k) \cdot g(k)$.

Thus, you want to know the value of this sum for the known values of $n$ and $p$. Or do you?

입력

The first line of the input contains a single integer n ($2 \le n \le 6 \cdot 10^5$) --- the number of participants.

The second line contains two integers $a$ and $b$ ($1 \le a < b \le 100$) --- the numerator and the denominator of fraction $\frac{a}{b} = p$.

출력

It can be shown that the answer can be represented as $\frac{P}{Q}$, where $P$ and $Q$ are coprime integers and $Q \not\equiv 0 \pmod{998244353}$.

Output the value of $P \cdot Q^{-1}$ modulo $998244353$.

예제 입력 1

4
2 6

예제 출력 1

517608191

힌트

In the example test case, $f(1) = \frac{5}{9}$, $f(2) = \frac{35}{81}$ and $f(3) = \frac{5}{9}$. Also, $g(1) = 1$, $g(2) = 3$ and $g(3) = 11$. Thus, the answer is $\frac{5}{9} \cdot 1 + \frac{35}{81} \cdot 3 + \frac{5}{9} \cdot 11 = \frac{215}{27}$.