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
//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define pp pair<int,int>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define ld long double
#define al(a) (a).begin(),(a).end()
#define mk make_pair
#define check cout<<"?"<<endl;

ll MOD=1000000007;
ll mod=998244353;
int inf=1000001000;
ll INF=1e18+5;

int main(){
    int n,k; cin>>n>>k;
    string s,sr,t; cin>>s;
    sr=s; reverse(al(sr));
    if(k==1){
        t=s+sr;
        string temp="{";
        rep(i,n+1){
            string cur=s;
            rep(j,n) cur[j]=t[i+j];
            if(temp>cur) temp=cur;
        }
        cout<<temp<<endl;
        return 0;
    }
    t=s+sr;
    string temp="{";
    rep(i,n+1){
        string cur=s;
        rep(j,n) cur[n-j-1]=t[i+j];
        if(temp>cur) temp=cur;
    }
    int d=0,c;
    rep(i,n){
        if(temp[i]==temp[0]) d++;
        else break;
    }
    c=d;
    rep(i,k-1){
        d*=2;
        if(d>n){
            rep(i,n) cout<<temp[0];
            cout<<endl;
            return 0;
        }
    }
    rep(i,d) cout<<temp[0];
    rep(i,n-d) cout<<temp[i+c];
    cout<<endl;
}
