{"problem":{"name":"Best-of-(2n-1)","description":{"content":"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 probabil","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"m_solutions2019_c"},"statements":[{"statement_type":"Markdown","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.)\n\n## Constraints\n\n*   $1 \\leq N \\leq 100000$\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.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $A$ $B$ $C$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"m_solutions2019_c","tags":[],"sample_group":[["1 25 25 50","2\n\nSince $N=1$, they will repeat the game until one of them wins. The expected number of games played is $2$."],["4 50 50 0","312500008\n\n$C$ may be $0$."],["1 100 0 0","1\n\n$B$ may also be $0$."],["100000 31 41 28","104136146"]],"created_at":"2026-03-03 11:01:14"}}