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.
n=+readline()
function gcd(a,b){
    if (!b)
        return a;
    return gcd(b,a%b)
}
for (t=0;t<n;t++){
    s=readline().split(' ')
    a=+s[0]
    b=+s[1]
    g=gcd(a,b)
    b/=g
    ans=1
    for (j=2;j*j<=b;j++){
        p=1
        while(b%j==0){
           b/=j
           p*=j
        }
        if (p>1)
            ans*=(p-p/j)
    }
    if (b>1)
    ans=ans*(b-1)
    print(ans)
}