1295_D. Same GCDs
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.
```python
import sys, math

for ii in range(int(input())):
    a,m = map(int,input().split())
    g = math.gcd(a,m)
    m=int(m/g)
    ans = m
    for i in range(2,int(math.sqrt(m))+1):
        if m%i==0:
            ans-=(ans/i)
        while m%i==0:
            m=int(m/i)
    if m>1:
        ans-=ans/m
    print(int(ans))
#3SUPE
```