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;

int main(){
	ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	int n, k;
	cin >> n >> k;
	string s;
	cin >> s;
	k = min(k, 15);
	char c = 'z';
	for(char x : s){
		c = min(c, x);
	}
	string t = s;
	reverse(t.begin(), t.end());
	string s1 = s + t;
	string best = s;
	for(int i = 0; i < n; i++){
		if(s[i] == c){
			int j = i;
			while(j > 0 && s[j-1] == c) j -= 1;
			int res = (i - j + 1) << (k-1);
			int pos = i+1;
			if(i == n-1){
				res = res << 1;
				pos = 2*n-j;
			}
			res = min(res, n);
			string ans(res, c);
			ans += s1.substr(pos, n - res);
			best = min(best, ans);
		}
	}
	cout << best << '\n';
}