CF908D.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 .

给你三个整数 $k$、$p_a$ 和 $p_b$。

你将按如下算法构造一个序列：初始时，序列为空。每一秒，执行以下操作：以概率 $\frac{p_a}{p_a + p_b}$ 在序列末尾添加字符 'a'；否则（即以概率 $\frac{p_b}{p_a + p_b}$）在序列末尾添加字符 'b'。

当序列中至少包含 $k$ 个子序列 'ab' 时，停止构造过程。求最终序列中子序列 'ab' 的期望出现次数。可以证明该期望值可表示为 $\frac{P}{Q}$，其中 $P$ 与 $Q$ 互质，且 $Q \not\equiv 0 \pmod{10^9+7}$。请输出 $\frac{P}{Q} \bmod (10^9+7)$ 的值。

The first line will contain three integers integer k, p__a, p__b (1 ≤ k ≤ 1 000, 1 ≤ p__a, p__b ≤ 1 000 000).

第一行包含三个整数 $k$、$p_a$、$p_b$（$1 \leq k \leq 1\,000$，$1 \leq p_a, p_b \leq 1\,000\,000$）。

Print a single integer, the answer to the problem.

输出一个整数，即该问题的答案。

The first sample, we will keep appending to our sequence until we get the subsequence 'ab' at least once. For instance, we get the sequence 'ab' with probability 1/4, 'bbab' with probability 1/16, and 'aab' with probability 1/8. Note, it's impossible for us to end with a sequence like 'aabab', since we would have stopped our algorithm once we had the prefix 'aab'.

The expected amount of times that 'ab' will occur across all valid sequences is 2.

For the second sample, the answer is equal to .

第一个样例中，我们将不断向序列末尾追加字符，直到子序列 'ab' 至少出现一次为止。例如，得到序列 'ab' 的概率为 $1/4$，得到 'bbab' 的概率为 $1/16$，得到 'aab' 的概率为 $1/8$。注意，序列 'aabab' 是不可能作为最终结果出现的，因为当我们的前缀变为 'aab' 时，算法就会停止（此时已包含子序列 'ab'）。

所有合法序列中 'ab' 出现次数的期望值为 $2$。

第二个样例的答案等于 。