Kth Root.cpp

/* Hacker Blocks */
/* Title - Kth Root */
/* Created By - Akash Modak */
/* Date - 25/06/2020 */

// You are given two integers n and k. Find the greatest integer x, such that, x^k <= n.

// Input Format
// First line contains number of test cases, T. Next T lines contains integers, n and k.

// Constraints
// 1<=T<=10 1<=N<=10^15 1<=K<=10^4

// Output Format
// Output the integer x

// Sample Input
// 2
// 10000 1
// 1000000000000000 10
// Sample Output
// 10000
// 31
// Explanation
// For the first test case, for x=10000, 10000^1=10000=n

#include<iostream>
#include<cmath>
using namespace std;
int main() {
	int t;
	cin>>t;
	while(t--){
		long long int n,k;
		cin>>n>>k;
		long long int s=1,e=n;
		long long int ans = 0;
		while(s<=e){
			long long int mid = (s+e)/2;
			if(pow(mid,k)<=n){
				ans = max(ans,mid);
				s=mid+1;
			}
			else
			e=mid-1;

		}
		cout<<ans<<endl;
	}
	return 0;
}