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>
#define l_ength size
const int inf = (1<<30);
const int mod = 1000000007;
using ll = long long;
using namespace std;

int main(){
	int n, k; cin >> n >> k;
	string str; cin >> str;
	char c_min = 'z';
	for( char c : str ) c_min = min( c, c_min );
	if( k < 14 ){
		string tmp = "";
		while( k-- ){
			tmp += str; reverse( str.begin(), str.end() );
			tmp += str;
			if( k > 0 ) reverse( tmp.begin(), tmp.end() );
			vector<string> candy;
			for( int i = 0; i <= n; ++i ){
				candy.push_back( tmp.substr(i, n) );
			}
			sort( candy.begin(), candy.end() );
			str = candy.front();
			if( k > 0 ) reverse( str.begin(), str.end() );
			// cout << str << endl;
			tmp = "";
			if( k == 0 ){
				cout << str << endl;
				return 0;
			}
		}
	}
	else{
		string ans = "";
		while( n-- ){
			ans += c_min; 
		}
		cout << ans << endl;
	}
	return 0;
}