1205. Power of Cryptography

Given an integer n ³ 1 and an integer p ³ 1 you are to write a program that determines , the positive n - th root of p. There always exists such integer k that kⁿ = p.

Input. Consists of two numbers n and p (1 £ n £ 300, 1 £ p < 10¹⁰¹). It is known that there always exists an integer k (1 ≤ k ≤ 10⁹) such that kⁿ = p.

Output. Print the value , i.e. the number k such that kⁿ = p.

Sample input

7 4357186184021382204544

Sample output

1234

SOLUTION

mathematics

Algorithm analysis

It is known that = = = . Subject to the constraints on numbers n, p and k just use double type for their declaration and calculate the value of . In C language it will be written as exp(log(p)/n).

Example

For the given test we have = 1234.

Algorithm realization

Read the values of n and p, calculate and print .

scanf("%lf %lf",&n,&p);

res = exp(log(p)/n);

printf("%.0lf\n",res);

Java realization

import java.util.Scanner;

public class Main

{

public static void main(String[] args)

{

Scanner con = new Scanner(System.in);

double n = con.nextDouble();

double p = con.nextDouble();

double res = Math.pow(p,1/n);

System.out.println((int)(res+0.5));

}

}