题目描述
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 choose?
Definition of common divisor
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Definition of being coprime
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
Definition of dividing
An integer x is said to divide another integer y when there exists an integer $\alpha$ such that $y = \alpha x$.
Constraints
- All values in input are integers.
- $1 \leq A, B \leq 10^{12}$
Input
Input is given from Standard Input in the following format:
A B
Output
Print the maximum number of divisors that can be chosen to satisfy the condition.
Examples
Input
12 18
Output
3
Input
420 660
Output
4
Input
1 2019
Output
1
输入格式
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输出格式
见题面