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 os,sys,math,random

T = int(input())
a, m, g = 0, 0, 0
a0, m0 = 0, 0

def de(n):
    r = int(n**0.5) + 1
    res = []
    for i in range(2, r):
        if n % i == 0:
            res.append(i)
            while n % i == 0:
                n /= i
    if n >= 2:
        res.append(n)
    return res

def cal(ub, ds):
    ld = len(ds)
    res = 0
    for i in range(1, (1<<ld)):
        dv, dn = 1, 0
        for j in range(0, ld):
            if i & (1<<j) > 0:
                dv *= ds[j]
                dn += 1

        cur = int(ub / dv) + 1
        if(dn % 2 == 0):
            cur *= -1
        res += cur
    return ub + 1 - res


def solve():
    global a,m,g
    g = math.gcd(a, m) 
    a, m = int(a/g), int(m/g)
    lb, ub = a - 1, m + a - 1
    ds = de(m)
    return cal(ub, ds) - cal(lb, ds)


for _ in range(T):
    a, m = map(int, input().split())
    a0, m0 = a, m
    print(solve())

