{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   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*   $K \\geq 1$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$A$ $B$ $K$"},{"iden":"sample input 1","content":"8 12 2"},{"iden":"sample output 1","content":"2\n\nThree positive integers divides both $8$ and $12$: $1, 2$ and $4$. Among them, the second largest is $2$."},{"iden":"sample input 2","content":"100 50 4"},{"iden":"sample output 2","content":"5"},{"iden":"sample input 3","content":"1 1 1"},{"iden":"sample output 3","content":"1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}