You are given two integers a and m. Calculate the number of integers x such that 0 ≤ x < m and \gcd(a, m) = \gcd(a + x, m).

Note: \gcd(a, b) is the greatest common divisor of a and b.

Input

The first line contains the single integer T (1 ≤ T ≤ 50) — the number of test cases.

Next T lines contain test cases — one per line. Each line contains two integers a and m (1 ≤ a < m ≤ 10^{10}).

Output

Print T integers — one per test case. For each test case print the number of appropriate x-s.

Example

Input


3
4 9
5 10
42 9999999967


Output


6
1
9999999966

Note

In the first test case appropriate x-s are [0, 1, 3, 4, 6, 7].

In the second test case the only appropriate x is 0.
from math import gcd
from itertools import combinations

def main():
    T = int(input().strip())
    for _ in range(T):
        a, m = [int(s) for s in input().strip().split()]
        d = gcd(a, m)
        a //= d
        m //= d

        factors = set()
        tmp = m
        while tmp % 2 == 0:
            factors.add(2)
            tmp //= 2
        i = 3
        while i ** 2 <= tmp:
            while tmp % i == 0:
                factors.add(i)
                tmp //= i
            i += 2
        if tmp > 1:
            factors.add(tmp)
        
        result = 0
        for i in range(len(factors) + 1):
            for t in combinations(factors, i):
                d = 1
                for j in t:
                    d *= j
                
                result += (-1) ** i * ((a+m-1)//d - (a-1)//d)
        print(result)


main()
