{"problem":{"name":"K-th Common Divisor","description":{"content":"You are given positive integers $A$ and $B$. Find the $K$\\-th largest positive integer that divides both $A$ and $B$. The input guarantees that there exists such a number.","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc120_b"},"statements":[{"statement_type":"Markdown","content":"You are given positive integers $A$ and $B$.\nFind the $K$\\-th largest positive integer that divides both $A$ and $B$.\nThe input guarantees that there exists such a number.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq A, B \\leq 100$\n*   The $K$\\-th largest positive integer that divides both $A$ and $B$ exists.\n*   $K \\geq 1$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$A$ $B$ $K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc120_b","tags":[],"sample_group":[["8 12 2","2\n\nThree positive integers divides both $8$ and $12$: $1, 2$ and $4$. Among them, the second largest is $2$."],["100 50 4","5"],["1 1 1","1"]],"created_at":"2026-03-03 11:01:14"}}