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.

Examples

Input

5 1
bacba


Output

aabca


Input

10 2
bbaabbbaab


Output

aaaabbaabb
#include <bits/stdc++.h>

using namespace std;

const int MX = 10000;

string solve(string S, int k) {
	if (k == 0) return S;
	
	while (k--) {
		int i = (int)S.size() - 1, cnt = 0;
		while (i >= 0 && S[i] == S.back()) i--, cnt++;
		
		if (i == -1) break;
		
		S = S.substr(cnt) + string(cnt, S.back());
	}
	
	reverse(S.begin(), S.end());
	
	return S;
}

char s[MX];

int main() {
	int n, k;
	ignore = scanf("%d %d %s", &n, &k, s);
	
	for (int i = n, j = n - 1; i < 2 * n; i++, j--) s[i] = s[j];
	
	string ans(n, 'z');
	for (int i = 0; i <= n; i++) {
		string S(s + i, s + i + n);
		ans = min(solve(S, k - 1), ans);
	}
	
	printf("%s\n", ans.c_str());
	
	return 0;
}
