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 sys, math, itertools
input = sys.stdin.readline

T = int(input())

def gcd(a, b):
    if a < b: a, b = b, a
    while b:
        r = a % b
        a, b = b, r
    return a

for _ in range(T):
    a, m = map(int, input().split())
    g = gcd(a,m)

    D = set()
    k = m // g
    while True:
        if k == 1: break
        q = k
        for i in range(2, int(math.sqrt(k)) + 2):
            if k % i == 0:
                D.add(i)
                k //= i
                break
        if k == q:
            D.add(k)
            break

    P = a + m - 1
    Q = a - 1

    ans = P // g
    diff = Q // g
    for i in range(1, len(D) + 1):
        
        for q in itertools.combinations(D, i):
            qq = 1
            for z in q:
                qq *= z

            if i & 1:
                ans -= P // (qq * g)
                diff -= Q // (qq * g)
            else:
                ans += P // (qq * g)
                diff += Q // (qq * g)


    print(ans - diff)

