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):
    while 1:
        b=b%a
        if b==0:
            return a
        a=a%b
        if a==0:
            return b
t=int(input())
for i2 in range(t):
    a,m=map(int,input().split())
    k=gcd(a,m)
    ans=m//k
    x=m//k
    i=1
    for i in range(2,math.ceil(x**(1/2))+1):
        if x%i==0:
            while x%i==0:
                x//=i
            ans-=ans//i
    if x>=2:
        ans-=ans//x
    print(ans)