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;
const int N=1e4+10;

int n,k,L[N];
string s;

int main() {
	cin>>n>>k>>s;
	char mn=*min_element(s.begin(),s.end());
	string t=s;reverse(t.begin(),t.end());t=s+t;
	for(int i=0;i<n+n;i++) {
		if(i&&t[i]==mn) L[i]=L[i-1]+1;
		else L[i]=0;
	}
	int mx=*max_element(L,L+n+n),len=mx;
	while(k>1&&len<n) --k,len<<=1;
	if(len>=n) cout<<string(n,mn);
	else {
		string ans;
		for(int i=n-1;i<n+n;i++)
			if(L[i]==mx) {
				string tmp=string(len,mn)+t.substr(n+n-1-i+mx,n-len);
				if(ans.empty()||ans>tmp) ans=tmp;
			}
		cout<<ans;
	}
	return 0;
}
