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
import math

t=int(input())

for test in range(t):
    a,m=map(int,input().split())
    GCD=math.gcd(a,m)

    x=m//GCD
    L=int(math.sqrt(x))
    FACT=dict()
    for i in range(2,L+2):
        while x%i==0:
            FACT[i]=FACT.get(i,0)+1
            x=x//i
    if x!=1:
        FACT[x]=FACT.get(x,0)+1

    ANS=m//GCD
    for f in FACT:
        ANS=ANS*(f-1)//f
    print(ANS)
                
            
            
        
    
    
