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<iostream>
#include<algorithm>
#include<vector>
using namespace std;
typedef long long ll;
#define mod 1000000007
#define chmin(a,b) a=min(a,b)
int n,k;
string s,p;
void doubl(){
    p=s;
    string t=s; reverse(t.begin(),t.end());
    s+=t;
}
int main(){
  cin>>n>>k>>s;
  for(int i=0;i<min(k-1,100);i++){
      doubl();
      for(int i=0;i<=n;i++){
          chmin(p,s.substr(i,n));
      }
      reverse(p.begin(),p.end());
      s=p;
  }
  doubl();
  for(int i=0;i<n;i++)chmin(p,s.substr(i,n));
  cout<<p<<endl;
  return 0;
}
