Problem: You are given a string t consisting of n lowercase Latin letters and an integer number k.

Let's define a substring of some string s with indices from l to r as s[l ... r].

Your task is to construct such string s of minimum possible length that there are exactly k positions i such that s[i ... i + n - 1] = t. In other words, your task is to construct such string s of minimum possible length that there are exactly k substrings of s equal to t.

It is guaranteed that the answer is always unique.

Input

The first line of the input contains two integers n and k (1 ≤ n, k ≤ 50) — the length of the string t and the number of substrings.

The second line of the input contains the string t consisting of exactly n lowercase Latin letters.

Output

Print such string s of minimum possible length that there are exactly k substrings of s equal to t.

It is guaranteed that the answer is always unique.

Examples

Input

3 4
aba


Output

ababababa


Input

3 2
cat


Output

catcat

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<string> v, vf;
int mini = 1e9;
int main() {
  int n, k;
  string t, myans;
  cin >> n >> k >> t;
  k--;
  if (!k) {
    cout << t;
    return 0;
  }
  for (int i = 0; i < n; ++i) {
    string ans = "";
    for (int j = i; j < n; ++j) {
      ans += t[j];
      v.push_back(ans);
    }
  }
  for (int i = 0; i < v.size(); ++i) {
    string nw = t + v[i];
    int cnt = 0;
    for (int j = 0; j < nw.size(); ++j) {
      string nwans;
      for (int k = j; k < nw.size(); ++k) {
        nwans += nw[k];
        if (nwans == t) {
          cnt++;
          break;
        }
      }
    }
    if (cnt == 2) {
      vf.push_back(nw);
    }
  }
  for (int i = 0; i < vf.size(); ++i) {
    if (vf.size() < mini) {
      mini = vf[i].size();
      myans = vf[i];
    }
  }
  string add = "";
  for (int i = n; i < myans.size(); ++i) {
    add += myans[i];
  }
  for (int i = 0; i < k - 1; ++i) {
    myans += add;
  }
  cout << myans;
  return 0;
}