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 <iomanip>
#include <cstdio>
#include <vector>
#include <string>
#include <algorithm>
#include <map>
#include <set>
 
using namespace std;
typedef long long ll;

int N, K;
string S;

string cv;

int main()
{
    ios_base::sync_with_stdio(0);
    
    cin >> N >> K >> S;
    for (int i = N - 1; i >= 0; i--)
        S += S[i];

    cv = S.substr(0, N);
    for (int i = 1; i <= N; i++)
        cv = min (cv, S.substr(i, N));
    if (K == 1)
    {
        cout << cv << "\n";
        return 0;
    }

    K--;
    //cout << cv << endl;
    int na = 1;
    while (na < N && cv[na] == cv[na-1])
        na++;

    int ntot = na;
    for (int i = 0; i < K; i++)
    {
        ntot = min (N, ntot * 2);
        if (ntot == N) break;
    }

    for (int i = 0; i < ntot; i++)
        cout << cv[0];
    for (int i = 0; i < N - ntot; i++)
        cout << cv[i+na];
    cout << "\n";
}