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;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, m, x = 0, y = 0, c = 0, ans = 0;
  bool f = true;
  string s;
  cin >> n >> m;
  cin >> s;
  for (int i = 1; i < s.size(); i++) {
    if (s[i] != s[i - 1]) f = false;
  }
  if (f) {
    char c = s[0];
    for (int i = 0; i < m - 1; i++) s += c;
    cout << s << endl;
    return 0;
  }
  int j = 0;
  for (int i = 1; i < s.size(); i++) {
    if (s[i] == s[j]) {
      bool ff = true;
      for (int k = i; k < s.size(); k++) {
        if (s[k] == s[j])
          j++;
        else {
          j = 0;
          ff = false;
          break;
        }
      }
      if (ff) break;
    }
  }
  string res = "";
  if (j) {
    res += s;
    for (int i = 0; i < m - 1; i++) {
      for (int k = j; k < n; k++) res += s[k];
    }
    cout << res << endl;
  } else {
    for (int i = 0; i < m; i++) res += s;
    cout << res << endl;
    return 0;
  }
  return 0;
}