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 MAXN=5010;
char s[MAXN],ans[MAXN],t[MAXN<<1];
int n,k;
inline void change(register int x)
{
	for(register int i=1;i<=n;i++) t[(n<<1)-i+1]=t[i];
	memmove(t+1,t+x,n);
	return;
}
inline void work(register int l,register int r)
{
	memcpy(t+1,s+1,n);
	if(k==1) change(l);
	else
	{
		register int now=k;
		if(r!=n) change(n-l+2),l=n+l-r,r=n,now--;
		for(register int i=1;i<now&&l>1;i++) change(n-l+2),l=(l<<1)-n-1;
		l=max(l,1);
		change(l);
	}
	if(strcmp(t+1,ans+1)<0) memcpy(ans+1,t+1,n);
}
int main()
{
	scanf("%d%d%s",&n,&k,s+1);
	memcpy(ans+1,s+1,n);
	for(register int i=1;i<=n;)
	{
		register int ri=i;
		while(s[ri]==s[i]) ri++;
		work(i,ri-1);
		i=ri;
	}
	puts(ans+1);
	return 0;
}