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 os, sys, bisect, copy
from collections import defaultdict, Counter, deque
from functools import lru_cache   #use @lru_cache(None)
if os.path.exists('in.txt'): sys.stdin=open('in.txt','r')
#if os.path.exists('out.txt'): sys.stdout=open('out.txt', 'w')
#
def input(): return sys.stdin.readline()
def mapi(arg=0): return map(int if arg==0 else str,input().split())
#------------------------------------------------------------------
# gcd of x and y
def GCD(x, y): return GCD(y,x%y) if y else x
for _ in range(int(input())):
    a,m = mapi()
    m //=GCD(a,m)
    res = m
    den = 1
    for i in range(2,int(m**.5)+1):
        if m%i==0:
            while m%i==0:
                m//=i
            res*=(i-1)
            den*=i
    if m>1:
        res*=(m-1)
        den*=m
    print(res//den)