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 pir pair<int,int>
#define qmin(x,y) (x=min(x,y))
#define qmax(x,y) (x=max(x,y))
#define rsort(x,y) sort(x,y),reverse(x,y)
#define fr first
#define se second
using namespace std;
typedef long long ll;
const int Maxn=2100000;
const int inf=0x3f3f3f3f;

int n,k;
char s[Maxn];

signed main() {
    // freopen("test.in","r",stdin);
    scanf("%d%d",&n,&k);
    scanf("%s",s);
    for(int i=0;i<n;i++) s[i+n]=s[n-i-1];
    int temp=0;
    for(int i=1;i<=n;i++) {
        int flag=0;
        for(int j=0;j<n;j++)
            if(s[temp+j]<s[i+j]) break;
            else if(s[temp+j]>s[i+j]) {
                flag=1;
                break;
            }
        if(flag) temp=i; 
    }
    int sxz=1,nh=n;
    for(int i=1;i<n;i++) {
        if(s[temp+i]!=s[temp]) {
            nh=i;
            break;
        }
        sxz++;
    }
    for(int i=1;i<k&&sxz<=n;i++) sxz<<=1;
    qmin(sxz,n);
    for(int i=1;i<=sxz;i++) putchar(s[temp]);
    for(int i=0;i<n-sxz;i++) putchar(s[temp+nh+i]);
    return 0;
}
