#D11288. Same GCDs
Same GCDs
Same GCDs
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.
inputFormat
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}).
outputFormat
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.
样例
3
4 9
5 10
42 9999999967
6
1
9999999966