{"problem":{"name":"Only one of two","description":{"content":"You are given three positive integers $N$, $M$, and $K$. Here, $N$ and $M$ are different.   Print the $K$\\-th smallest positive integer divisible by **exactly one** of $N$ and $M$.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc341_d"},"statements":[{"statement_type":"Markdown","content":"You are given three positive integers $N$, $M$, and $K$. Here, $N$ and $M$ are different.  \nPrint the $K$\\-th smallest positive integer divisible by **exactly one** of $N$ and $M$.\n\n## Constraints\n\n*   $1 \\leq N, M \\leq 10^8$\n*   $1 \\leq K \\leq 10^{10}$\n*   $N \\neq M$\n*   $N$, $M$, and $K$ are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$ $K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc341_d","tags":[],"sample_group":[["2 3 5","9\n\nThe positive integers divisible by exactly one of $2$ and $3$ are $2, 3, 4, 8, 9, 10, \\ldots$ in ascending order.  \nNote that $6$ is not included because it is divisible by both $2$ and $3$.  \nThe fifth smallest positive integer that satisfies the condition is $9$, so we print $9$."],["1 2 3","5\n\nThe numbers that satisfy the condition are $1, 3, 5, 7, \\ldots$ in ascending order."],["100000000 99999999 10000000000","500000002500000000"]],"created_at":"2026-03-03 11:01:14"}}