Problem:
Score : 300 points

Problem Statement

There are N integers a_1, a_2, ..., a_N not less than 1.
The values of a_1, a_2, ..., a_N are not known, but it is known that a_1 \times a_2 \times ... \times a_N = P.

Find the maximum possible greatest common divisor of a_1, a_2, ..., a_N.

Constraints

1 \leq N \leq 10^{12}

1 \leq P \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N P

Output

Print the answer.

Sample Input 1

3 24

Sample Output 1

2

The greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.

Sample Input 2

5 1

Sample Output 2

1

As a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.

Sample Input 3

1 111

Sample Output 3

111

Sample Input 4

4 972439611840

Sample Output 4

206

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun prime-factorization (n)
  (let ((ans '()))
    (labels ((divide (m i c)
		     (unless (zerop (rem m i))
		       (return-from divide (values m (cons i c))))
		     (divide (/ m i) i (1+ c)))
	     (take-apart (m i)
			 (when (= m 1)
			   (return-from take-apart ans))

			 (when (< (sqrt m) i)
			   (return-from take-apart
			     (setf ans (append ans (list (cons m 1))))))

			 (if (zerop (rem m i))
			    (multiple-value-bind (m2 part) (divide m i 0)
			      (setf ans (append ans (list part)))
			      (take-apart m2 (1+ i)))
			    (take-apart m (1+ i)))))
      (take-apart n 2)
      ans)))

(defun caddi2018c ()
  (let* ((n (read)) (p (read)))
    (reduce #'*
	    (mapcar (lambda (x) (expt (car x) (floor (cdr x) n)))
		    (prime-factorization p)))))

(format t "~a~%" (caddi2018c))