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.
def gcd(x,y):
    if(y==0):
        return x
    return gcd(y,x%y)


M=10**5+100
prime=[True]*M
for i in range(1,M):
        if(i==1):
            prime[i]=False
        else:
            for j in range(2*i,M,i):
                prime[j]=False


for t in range(int(input())):
    a,b=map(int,input().split())
    m=gcd(a,b)
    b//=m
    total=b
    for i in range(1,M):
        if(prime[i]==True and b%i==0):

            total//=i
            total*=(i-1)
            while(b%i==0):
                b//=i
    if(b>1):
        total//=b
        total*=(b-1)
    print(total)