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 C (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>
#include <inttypes.h>

int main(void) {
	uint64_t N, P;
	int mikakosi = 0, i;
	uint64_t asumi[256];
	uint64_t iguti[256];
	uint64_t mizuhasu, mamegu;
	uint64_t mikisinn, sinntasu;
	if (scanf("%" SCNu64 "%" SCNu64, &N, &P) != 2) return 1;
	for (mizuhasu = 2, mamegu = P; mizuhasu * mizuhasu <= mamegu; mizuhasu++) {
		if (mamegu % mizuhasu == 0) {
			uint64_t tomatu = 0;
			while (mamegu % mizuhasu == 0) {
				tomatu++;
				mamegu /= mizuhasu;
			}
			asumi[mikakosi] = mizuhasu;
			iguti[mikakosi] = tomatu;
			mikakosi++;
		}
	}
	if (mamegu > 1) {
		asumi[mikakosi] = mamegu;
		iguti[mikakosi] = 1;
		mikakosi++;
	}

	sinntasu = 1;
	for (i = 0; i < mikakosi; i++) {
		uint64_t minngosu = iguti[i] / N;
		for (mikisinn = 0; mikisinn < minngosu; mikisinn++) sinntasu *= asumi[i];
	}
	printf("%" PRIu64 "\n", sinntasu);

	return 0;
}