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 math

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

def phi(val):
    ret = 1
    for i in range(2,int(math.sqrt(val)) + 1):
        if val % i == 0:
            c = 0
            while val % i == 0:
                val //= i
                c += 1
            ret *= (i - 1)
            for j in range(1,c):
                ret *= i
    if val > 1:
        ret *= (val - 1)
    return ret

for _ in range(int(input())):
    a,m = map(int,input().split())
    g = __gcd(a,m)
    print(phi(m // g))
    
