{"raw_statement":[{"iden":"problem statement","content":"Takahashi and Aoki will play a game. They will repeatedly play it until one of them have $N$ wins in total.\nWhen 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.\nWe 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.)"},{"iden":"constraints","content":"*   $1 \\leq N \\leq 100000$\n*   $0 \\leq A,B,C \\leq 100$\n*   $1 \\leq A+B$\n*   $A+B+C=100$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $A$ $B$ $C$"},{"iden":"sample input 1","content":"1 25 25 50"},{"iden":"sample output 1","content":"2\n\nSince $N=1$, they will repeat the game until one of them wins. The expected number of games played is $2$."},{"iden":"sample input 2","content":"4 50 50 0"},{"iden":"sample output 2","content":"312500008\n\n$C$ may be $0$."},{"iden":"sample input 3","content":"1 100 0 0"},{"iden":"sample output 3","content":"1\n\n$B$ may also be $0$."},{"iden":"sample input 4","content":"100000 31 41 28"},{"iden":"sample output 4","content":"104136146"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}