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 <cstdio>
#include <cstring>
#include <vector>
#include <set>
#include <cstdlib>
#include <map>
#include <iostream>
#include <algorithm>

#define X first
#define Y second
#define PB push_back

using namespace std;

typedef long long ll;
typedef pair < int, int > pii;
typedef vector < int > vi;

const int N = 2e5 + 500;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
const int BASE = 31337;

string S;
int k, n;

int main(){
	cin >> n >> k >> S;
	for(int i = 0;i < k;i++){
		string U = S;
		reverse(S.begin(), S.end());
		U += S;
		reverse(S.begin(), S.end());
		for(int i = 1;i <= n;i++){
			if(U.substr(i, n) < S)
				S = U.substr(i, n);
		}
		if(i != k - 1)
			reverse(S.begin(), S.end());
		bool gotov = 1;
		for(char c : S)
			gotov &= (c == S[0]);
		if(gotov)
			break;
	}
	cout << S << endl;
	return 0;
}
