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
input = sys.stdin.readline

def gcd(a,b):
    if b == 0:
        return a
    else:
        return gcd(b,a%b)

def prime_factor(n):
    ass = []
    for i in range(2,int(n**0.5)+1):
        while n % i==0:
            ass.append(i)
            n = n//i
    if n != 1:
        ass.append(n)
    return list(set(ass))



t = int(input())

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

    g = gcd(a,m)

    a = a//g
    m = m//g

    p = prime_factor(m)

    k = len(p)


    res = m

    for i in range(1,1<<k):
        cp = 0

        pri = 1
        for j in range(k):
            if (i>>j)&1 == 1:
                pri *= p[j]
                cp += 1
        
        
        if a%pri == 0:
            cnt = m//pri + 1
        else:
            start = (a//pri+1)*pri
            if start > a + m -1 :
                cnt = 0
            else:
                cnt = ((a+m-start)//pri+1)

        res += ((-1)**cp)*cnt

    print(res)


