{"problem":{"name":"increment of coins","description":{"content":"We have a bag containing $A$ gold coins, $B$ silver coins, and $C$ bronze coins. Until the bag contains $100$ coins of the same color, we will repeat the following operation: Operation: Randomly take ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc184_d"},"statements":[{"statement_type":"Markdown","content":"We have a bag containing $A$ gold coins, $B$ silver coins, and $C$ bronze coins.\nUntil the bag contains $100$ coins of the same color, we will repeat the following operation:\nOperation: Randomly take out one coin from the bag. (Every coin has an equal probability of being chosen.) Then, put back into the bag two coins of the same kind as the removed coin.\nFind the expected value of the number of times the operation is done.\n\n## Constraints\n\n*   $0 \\leq A,B,C \\leq 99$\n*   $A+B+C \\geq 1$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$A$ $B$ $C$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc184_d","tags":[],"sample_group":[["99 99 99","1.000000000\n\nNo matter what coin we take out in the first operation, the bag will contain $100$ coins of that kind."],["98 99 99","1.331081081\n\nWe will do the second operation only if we take out a gold coin in the first operation. Thus, the expected number of operations is $2\\times \\frac{98}{98+99+99}+1\\times \\frac{99}{98+99+99}+1\\times \\frac{99}{98+99+99}=1.331081081\\ldots$"],["0 0 1","99.000000000\n\nEach operation adds a bronze coin."],["31 41 59","91.835008202"]],"created_at":"2026-03-03 11:01:14"}}