时间限制：C/C++/Rust/Pascal 2秒，其他语言4秒
空间限制：C/C++/Rust/Pascal 1024 M，其他语言2048 M
64bit IO Format: %lld
空间限制：C/C++/Rust/Pascal 1024 M，其他语言2048 M
64bit IO Format: %lld
题目描述
Bobo has recently been playing Dota2. Due to a new event, "Crownfall" in Dota2, Bobo received a number of 
Double Down Tokens. In ranked contests of Dota2, players receive 
MMR for wins and 
MMR for loses. MMR Double Down tokens are items that can be used \textbf{at the beginning of a ranked contest}, so that the MMR gained in this contest will be doubled (
for wins and 
for loses).
However, Bobo suspects that Dota2 uses the ELO matching system to balance the winrates of players so that he will receive exactly
wins and 
loses in the upcoming 
contests, and all possible combinations of wins and loses will appear with equal probability.
Now, Bobo wants to design a strategy to use some of the MMR Double Down tokens so that after the contests, the expected additional MMR gained using MMR Double Down Tokens(that is, the MMR change across all contests, subtracted by 
) is maximum. You need to find out this maximum expected value.
However, Bobo suspects that Dota2 uses the ELO matching system to balance the winrates of players so that he will receive exactly
Now, Bobo wants to design a strategy to use some of the
输入描述:
The only line of input containsintegers
.
输出描述:
Output an integer in one line, denoting the answer. Under the input constraints of this problem, it can be shown that the answer can be written as, where
and
are coprime integers and
. You need to output
as an answer, where
is the modular inverse of
.
示例1
说明
For the first sample test, the optimal strategy of Bobo is as follows: if the first game is a lost, Bobo will use the MMR Double Down token at the beginning of the second contest, so he will guarantee an additional MMR gain of; if the first game is a win, Bobo will not use any MMR double down token. The expected additional MMR gained using this strategy is
.