Given three numbers x,k and m, you need to find the value of $x^{x^{x^{.^{.^{.^x}}}}}$%m where number of x's in the expression are k. That is, if x=5,k=3 and m=3, then you need to compute $5^{5^5}$%3.

Constraints:
$1 \le T \le 10^5$
$1 \le m \le 10^7$
$1 \le k \le 10^{18}$
$m < x \le 10^8$ x is always a prime number

Format of the input file:
First line : T i.e number of testcases.
For each testcase :
First line : Three space separated integers x , k and m.

Format of the output file:
Print the answer for each test case in a separate line