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.
import math
 
def cal(x, y, z):
    return z // x - y // x
 
T = int(input())
 
while T:
    T -= 1
    a, m = map(int, input().split())
    k = math.gcd(a, m)
    
    x = (m - 1) // k
    n = m // k
    i = 2
    p = []
    while i * i <= m // k:
        if n % i == 0:
            while n % i == 0:
                n //= i
            p.append(i)
        i += 1
    if n > 1:
        p.append(n)
        
    res = 0
    for mask in range(1, 1<<len(p)):
        tmp = 1
        cnt = 0
        for i in range(len(p)):
            if mask & (1<<i):
                tmp *= p[i]
                cnt += 1
        if cnt % 2 == 1:
            res += cal(tmp, a//k, a//k + x)
        else:
            res -= cal(tmp, a//k, a//k + x)
    print(x + 1 - res)
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