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
t = int(input())


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

    b = m//gcd(a, m)

    p = set()
    pow = {}

    i = 2
    while (i*i<=b):
        while (b%i==0):
            if i not in p:
                p.add(i)
                pow[i] = 0
            pow[i]+=1
            b//=i
        i+=1
    if (b>1):
        p.add(b)
        pow[b] = 1

    ans = 1
    for prost in p:
        ans*=prost**(pow[prost]-1)*(prost-1)
    print(ans)