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 N 5010
using namespace std;
char in[N+N],out[N];
int id[N],nid[N];
int main(){
	int n,k;
	scanf("%d%d",&n,&k);
	scanf("%s",in);
	for(int i=n;i<n+n;i++) in[i]=in[i-n];
	reverse(in+n,in+n*2);
	if(k>1) reverse(in,in+n*2);
	for(int i=0;i<=n;i++){
		id[i]=i;
	}
	for(int i=n-1;i>=0;i--){
		int cnt[26]={};
		for(int j=0;j<=n;j++){
			cnt[in[j+i]-'a']++;
		}
		for(int j=1;j<26;j++) cnt[j]+=cnt[j-1];
		for(int j=n;j>=0;j--){
			int cur=in[id[j]+i]-'a';
			nid[--cnt[cur]]=id[j];
		}
		for(int j=0;j<=n;j++) id[j]=nid[j];
	}
	for(int i=0;i<n;i++) out[i]=in[id[0]+i];
	int pl=1;
	for(int i=1;out[i]==out[i-1];i++) pl++;
	char *rem=out+pl;
	while(k>1&&pl<n){
		pl*=2;
		k--;
	}
	for(int i=0;i<min(n,pl);i++) putchar(out[0]);
	rem[max(n-pl,0)]=0;
	puts(rem);
	return 0;
}