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.
#
# author : Abhishek
#
import math


def phi(n):
    ans = n
    i = 2
    # print("ans " + str(ans))
    while i * i <= n:
        if n % i == 0 :
            ans //= i
            ans *= (i-1)
        while n % i == 0:
            # print(i)
            n //= i
        i+=1
        # print("ans " + str(ans))
    if n >= 2:
        ans //= n
        ans *= (n-1)
        n //= n
    # print("ans " + str(ans))
    return ans




for _ in range(int(input())):
    a,m = map(int,input().split()) 
    g = math.gcd(a,m)
    # print(a,m)
    # print(g)
    ans = phi(m/g)
    print(int(ans))