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 n, k;
string s, ss, ans;

string calc(string t){
    if (k==1) return t;
    string res=""; char c=t.back();
    while (t.size()&&t.back()==c){
        res+=t.back(); t.erase(--t.end());
    }
    for (int las=k-1;las--&&res.size()<n;){
        res=res+res; if (res.size()>n) res.resize(n);
    }
    while (res.size()<n){
        res+=t.back(); t.erase(--t.end());
    }
    return res;
}

int main(){
    cin>>n>>k>>s;
    ans="z"; ans[0]+=1;
    ss=s; reverse(ss.begin(),ss.end());
    ss=s+ss;
    for (int i=0;i+n<=ss.length();++i)
        ans=min(ans,calc(ss.substr(i,n)));
    cout<<ans<<endl;
}