{"raw_statement":[{"iden":"problem statement","content":"Given are positive integers $A$ and $B$.\nLet us choose some number of positive common divisors of $A$ and $B$.\nHere, any two of the chosen divisors must be coprime.\nAt most, how many divisors can we choose?\nDefinition of common divisor\n\nAn integer $d$ is said to be a common divisor of integers $x$ and $y$ when $d$ divides both $x$ and $y$.\n\nDefinition of being coprime\n\nIntegers $x$ and $y$ are said to be coprime when $x$ and $y$ have no positive common divisors other than $1$.\n\nDefinition of dividing\n\nAn integer $x$ is said to divide another integer $y$ when there exists an integer $\\alpha$ such that $y = \\alpha x$."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq A, B \\leq 10^{12}$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$A$ $B$"},{"iden":"sample input 1","content":"12 18"},{"iden":"sample output 1","content":"3\n\n$12$ and $18$ have the following positive common divisors: $1$, $2$, $3$, and $6$.\n$1$ and $2$ are coprime, $2$ and $3$ are coprime, and $3$ and $1$ are coprime, so we can choose $1$, $2$, and $3$, which achieve the maximum result."},{"iden":"sample input 2","content":"420 660"},{"iden":"sample output 2","content":"4"},{"iden":"sample input 3","content":"1 2019"},{"iden":"sample output 3","content":"1\n\n$1$ and $2019$ have no positive common divisors other than $1$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}