#D6621. SOLUTIONS Programming Contest - Best-of-(2n-1)
SOLUTIONS Programming Contest - Best-of-(2n-1)
SOLUTIONS Programming Contest - Best-of-(2n-1)
Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total.
When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows.
We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.)
Constraints
- 1 \leq N \leq 100000
- 0 \leq A,B,C \leq 100
- 1 \leq A+B
- A+B+C=100
- All values in input are integers.
Input
Input is given from Standard Input in the following format:
N A B C
Output
Print the expected number of games that will be played, in the manner specified in the statement.
Examples
Input
1 25 25 50
Output
2
Input
4 50 50 0
Output
312500008
Input
1 100 0 0
Output
1
Input
100000 31 41 28
Output
104136146
inputFormat
input are integers.
Input
Input is given from Standard Input in the following format:
N A B C
outputFormat
Output
Print the expected number of games that will be played, in the manner specified in the statement.
Examples
Input
1 25 25 50
Output
2
Input
4 50 50 0
Output
312500008
Input
1 100 0 0
Output
1
Input
100000 31 41 28
Output
104136146
样例
4 50 50 0312500008