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 <cstdio>
const int Maxn=10000;
char s[Maxn+5];
int n,k;
char *ans;
bool check(char *a,char *b){
	for(int i=1;i<=n;i++){
		if(a[i]<b[i]){
			return 1;
		}
		if(a[i]>b[i]){
			return 0;
		}
	}
	return 0;
}
int main(){
	scanf("%d%d",&n,&k);
	scanf("%s",s+1);
	while(s[++n]!='\0');
	n--;
	for(int i=1;i<=n;i++){
		s[(n<<1)-i+1]=s[i];
	}
	ans=s;
	for(int i=1;i<=n;i++){
		if(check(s+i-1,ans)){
			ans=s+i-1;
		}
	}
	int len=1;
	while(len<=n&&ans[++len]==ans[1]);
	len--;
	if(k>=15||(len*(1<<(k-1))>=n)){
		for(int i=1;i<=n;i++){
			putchar(ans[1]);
		}
		puts("");
	}
	else{
		int now=n-(len*(1<<(k-1)));
		for(int i=1;i<=(len*(1<<(k-1)));i++){
			putchar(ans[1]);
		}
		for(int i=1;i<=now;i++){
			putchar(ans[i+len]);
		}
		puts("");
	}
	return 0;
}
