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D - Disjoint Set of Common Divisors /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

AB の正の公約数の中からいくつかを選びます。

ただし、選んだ整数の中のどの異なる 2 つの整数についても互いに素でなければなりません。

制約

• 入力は全て整数である。
• 1 \leq A, B \leq 10^{12}

入力

A B


入力例 1

12 18


出力例 1

3


1218 の正の公約数は 1, 2, 3, 6 です。

122331 は互いに素なので、1, 2, 3 を選ぶことができ、このときが最大です。

入力例 2

420 660


出力例 2

4


入力例 3

1 2019


出力例 3

1


12019 の正の公約数は 1 しかありません。

Score : 400 points

Problem Statement

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.

Sample Input 1

12 18


Sample Output 1

3


12 and 18 have the following positive common divisors: 1, 2, 3, and 6.

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.

Sample Input 2

420 660


Sample Output 2

4


Sample Input 3

1 2019


Sample Output 3

1


1 and 2019 have no positive common divisors other than 1.