Expected Number of "ab" Subsequences

Problem Description

You are given three integers $k, p_a, p_b$. Initially there is an empty sequence. Each second, one of the following happens:

• with probability $\dfrac{p_a}{p_a + p_b}$, append the character a to the end;
• with probability $\dfrac{p_b}{p_a + p_b}$, append the character b to the end.

The process stops as soon as the sequence contains at least $k$ occurrences of the subsequence ab. Find the expected total number of ab subsequences at the end, and output the answer modulo $10^9+7$ as an integer.

Input Format

One line containing three integers $k, p_a, p_b$.

Output Format

One integer: the answer.

Sample Input 1

3 1 4

Sample Output 1

370000006

Sample Input 2

1 1 1

Sample Output 2

2

Constraints

For all data, $1 \le k \le 1000$ and $1 \le p_a, p_b \le 10^6$.