Problem:
Score : 1300 points

Problem Statement

Takahashi has a string S of length N consisting of lowercase English letters.
On this string, he will perform the following operation K times:

Let T be the string obtained by reversing S, and U be the string obtained by concatenating S and T in this order.

Let S' be some contiguous substring of U with length N, and replace S with S'.

Among the strings that can be the string S after the K operations, find the lexicographically smallest possible one.

Constraints

1 \leq N \leq 5000

1 \leq K \leq 10^9

|S|=N

S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

N K
S

Output

Print the lexicographically smallest possible string that can be the string S after the K operations.

Sample Input 1

5 1
bacba

Sample Output 1

aabca

When S=bacba, T=abcab, U=bacbaabcab, and the optimal choice of S' is S'=aabca.

Sample Input 2

10 2
bbaabbbaab

Sample Output 2

aaaabbaabb

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <cstdio>
#include <string>
#include <iostream>
#include <algorithm>
using namespace std;

#define R register

int N, K;
string s, rev, tmp, str;

int main() {
	cin >> N >> K >> s;
	rev = s, reverse(rev.begin(), rev.end());
	tmp = s + rev, reverse(tmp.begin(), tmp.end());
//cout << tmp << endl;
	str = tmp.substr(0, N);
	for(R int i = 1; i < N; ++i) {
		rev = tmp.substr(i, N);
		if(rev < str) str = rev;
	}
	reverse(str.begin(), str.end());
//cout << str << endl;
	for(R int i = 1, j; i < K; ++i) {
		for(j = N - 2; ~j; --j) if(str[j] != str[N - 1]) break;
		str = str + str.substr(j + 1, N);
//cout << str << endl;
		j = str.length();
		str = str.substr(j - N, N);
//cout << str << endl;
	}
	reverse(str.begin(), str.end());
 	cout << str;
 	return 0;
}