A. Divisiontime limit per test1 secondmemory limit per test512 megabytesinputstandard inputoutputstandard outputOleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:   p_i is divisible by x_i;  x_i is not divisible by q_i.  Oleg is really good at division and managed to find all the answers quickly, how about you?InputThe first line contains an integer t (1 \le t \le 50) — the number of pairs.Each of the following t lines contains two integers p_i and q_i (1 \le p_i \le 10^{18}; 2 \le q_i \le 10^{9}) — the i-th pair of integers.OutputPrint t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.ExampleInput
3
10 4
12 6
179 822
Output
10
4
179
NoteFor the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.For the second pair, where p_2 = 12 and q_2 = 6, note that   12 is not a valid x_2, since 12 is divisible by q_2 = 6;  6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.  The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
3
10 4
12 6
179 822

10 4 179 
['brute force', 'math', 'number theory', '*1500']