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 math
ts = int(input())

for case in range(ts):
    a, b = map(int, input().split())
    gc = math.gcd(a, b)
    koto = (b - 1) // gc
    baki = b // gc

    gc_lis = []

    for i in range(2, int(math.sqrt(baki)) + 1):
        if baki % i == 0:
            gc_lis.append(i)
            while baki % i == 0:
                baki //= i

    if baki > 1:
        gc_lis.append(baki)

    total = koto
    for j in range(1, (1<<len(gc_lis))):
        mul = 1
        cnt = 0
        for k in range(0, len(gc_lis)):
            if (j & (1<<k)) != 0:
                mul *= gc_lis[k]
                cnt += 1

        if cnt % 2 == 1:
            total -= (koto // mul)
        else:
            total += (koto // mul)

    print(total)