A11548 | New Year and Arbitrary Arrangement

You are given three integers $k$ , $p_{a}$ and $p_{b}$ .

You will construct a sequence with the following algorithm: Initially, start with the empty sequence. Each second, you do the following. With probability $p_{a}/(p_{a}+p_{b})$ , add 'a' to the end of the sequence. Otherwise (with probability $p_{b}/(p_{a}+p_{b})$ ), add 'b' to the end of the sequence.

You stop once there are at least $k$ subsequences that form 'ab'. Determine the expected number of times 'ab' is a subsequence in the resulting sequence. It can be shown that this can be represented by $P/Q$ , where $P$ and $Q$ are coprime integers, and . Print the value of .

The first line will contain three integers integer $k,p_{a},p_{b}$ ( $1<=k<=1000$ , $1<=p_{a},p_{b}<=1000000$ ).

Print a single integer, the answer to the problem.