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;
int main(){
    string s;int n,k,st=0,ed;
    cin>>n>>k>>s;
    if(k>30||(1<<(k-1))>=n){
        cout<<string(n,*min_element(s.begin(),s.end()))<<"\n";
        return 0;
    }
    string S=s;
    reverse(S.begin(),S.end());
    string T=s+S;
    for(int i=1;i<n;i++)
        if(T.substr(i,n)<T.substr(st,n))
            st=i;
    for(ed=st;ed-st+1<n&&T[st]==T[ed];ed++);
    for(int i=1;i<=((ed-st)<<(k-1))&&n;i++)cout<<T[st],n--;
    while(n--)cout<<T[ed++];
    cout<<"\n";
    return 0;
}