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 collections import defaultdict
from math import gcd


def Primes(M):
    prime = {i for i in range(2, M)}
    for i in range(2, M):
        if i in prime:
            for j in range(i*2, M, i):
                if j in prime:
                    prime.remove(j)
    return prime


primes = Primes(10**5)


def solve():
    a, m = map(int, input().split())
    g = gcd(a, m)
    G = m//g
    d = defaultdict(int)
    for p in primes:
        while G % p == 0:
            d[p] += 1
            G //= p
    if G > 1:
        d[G] = 1
    res = m//g
    for v in d.keys():
        res *= (v-1)
        res //= v
    print(res)
    return


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


if __name__ == "__main__":
    main()
