{"problem":{"name":"Disjoint Set of Common Divisors","description":{"content":"Given are positive integers $A$ and $B$. Let us choose some number of positive common divisors of $A$ and $B$. Here, any two of the chosen divisors must be coprime. At most, how many divisors can we c","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc142_d"},"statements":[{"statement_type":"Markdown","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 $y = \\alpha x$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq A, B \\leq 10^{12}$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$A$ $B$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc142_d","tags":[],"sample_group":[["12 18","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."],["420 660","4"],["1 2019","1\n\n$1$ and $2019$ have no positive common divisors other than $1$."]],"created_at":"2026-03-03 11:01:14"}}