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 N,K;
string s;
int main()
{
	scanf("%d%d",&N,&K);cin >> s;
	string t = s;
	reverse(t.begin(),t.end());s += t;
	string m = s.substr(0,N);
	for(int i = 1;i <= N;i ++)
		m = min(m,s.substr(i,N));
	int l = 1;
	while(l < m.size() && m[0] == m[l])
		l ++;
	long long k = l;K --;
	if(K > 17) k = N;
	else k <<= K;
	string ans = "";
	while(ans.size() < N && k > 0)
		k --,ans += m[0];
	ans += m.substr(l,N-ans.size());
	cout << ans << endl;
	return 0;
}