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;
int64_t N,K;
string s;
int main(){
  cin>>N>>K>>s;
  if(K==0)
    cout<<s<<endl;
  else{
  string S=s;
  vector<string>A(N+1);
  A[0]=S;
  for(int i=1;i<=N;i++){
  S.erase(0,1);
    S+=s.at(N-i);
  A[i]=S;
  }string S1=A[0];
    for(int i=1;i<=N;i++)
      if(A[i]<S1)S1=A[i];
    int sum=0;
    for(int i=0;i<N;i++){
    if(S1.at(i)==S1.at(0))sum++;
      else break;
    }int count=sum;
    for(int i=0;i<K-1;i++){
    sum*=2;if(N<=sum){sum=N;break;}
    }string ans="";
    for(int i=0;i<sum;i++)
      ans+=S1.at(0);
    for(int i=0;i<N-sum;i++)
      ans+=S1.at(count+i);
    cout<<ans<<endl;
  }
  return 0;
}