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
MAX = 10**5 + 100
PRIME = [True]*(MAX)
for v in range(1, MAX):
    if v == 1:
        PRIME[v] = False
        continue
    if PRIME[v] == True:
        for u in range(2*v, MAX, v):
            PRIME[u] = False
        continue


def solve():
    a, m = map(int, input().split())
    g = gcd(a, m)
    m //= g
    res = m
    for p in range(2, MAX):
        if PRIME[p] == True and m % p == 0:
            res //= p
            res *= (p - 1)
            while m % p == 0:
                m //= p
    if m > 1:
        res //= m
        res *= (m - 1)
    print(res)
    return


def main():
    testcase = int(input())
    for i in range(testcase):
        solve()
    return


if __name__ == "__main__":
    main()
