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;
using lint = long long;
const int mod = 1e9 + 7;
const int MAXN = 2000005;

int n, k;

string solve(string x, int k){
	int pos = x.size();
	while(pos > 0 && x[pos - 1] == x.back()) pos--;
	if(k >= 15){
		string s;
		s.resize(x.size());

		fill(s.begin(), s.end(), x.back());
		return s;
	}
	pos = x.size() - pos;
	pos = (pos << k) - pos;
	pos = min(pos, n);
	for(int i=0; i<pos; i++) x.push_back(x.back());
	reverse(x.begin(), x.end());
	x.resize(n);
	return x;
}

int main(){
	cin >> n >> k;
	string s; cin >> s;
	string ret = s;
	for(int i=0; i<=n; i++){
		string x = s.substr(i, n - i);
		string y = s.substr(n - i, i);
		reverse(y.begin(), y.end());
		if(i == 0) ret = min(ret, solve(x + y, k));
		else ret = min(ret, solve(x + y, k - 1));
	}
	cout << ret << endl;
}
