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, collections, sys
input = sys.stdin.readline
def totient(x):
    result = x
    p = 2
    while(p * p<= x):
        if (x % p == 0):
            while (x % p == 0):
                x = x // p 
            result = result * (1.0 - (1.0 / float(p))) 
        p = p + 1
    if (x > 1):
        result = result * (1.0 - (1.0 / float(x))) 
    return int(result)
for _ in range(int(input())):
    a, m = map(int, input().split())
    g = math.gcd(a, m)
    print(totient(m//g))