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.
from sys import stdin
import math

for case in range(int(stdin.readline())):
    a,m = [int(x) for x in stdin.readline().split()]

    aFactors = []
    mFactors = []
    
    for x in range(1, int(math.sqrt(a))+1):
        if a%x == 0:
            aFactors.append(x)
            aFactors.append(a//x)

    for x in range(1, int(math.sqrt(m))+1):
        if m%x == 0:
            mFactors.append(x)
            mFactors.append(m//x)

    aFactors.sort(reverse=True)
    mFactors.sort(reverse=True)
    
    mSet = set(mFactors)
    
    for x in aFactors:
        if x in mSet:
            gcd = x
            break

    a2 = a//gcd
    m2 = m//gcd

    m2Factors = []

    for x in range(1, int(math.sqrt(m2))+1):
        if m2%x == 0:
            if x != 1:
                m2Factors.append(x)
            if m2//x != x:
                m2Factors.append(m2//x)

    total = m2

    primeFactors = []
    for f in m2Factors:
        v = True
        for h in m2Factors:
            if h != f and f%h == 0:
                v = False
                break
        if v:
            primeFactors.append(f)
    #print(primeFactors)
    things = []
    for x in range(len(primeFactors)):
        for y in range(len(things)):
            things.append((things[y][0]*primeFactors[x], things[y][1]+1))
        things.append((primeFactors[x],0))
    for x,order in things:
        if order%2 == 1:
            total += (m2+a2-1)//x-(a2-1)//x
        else:
            total -= (m2+a2-1)//x-(a2-1)//x
    print(total)
            
    #print(total)

    
