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() {
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  int mark = 1;
  for (int i = 1; i < s.size(); i++) {
    if (s[i] != s[i - 1]) {
      mark = -1;
      break;
    }
  }
  if (mark == 1) {
    cout << s;
    for (int i = 1; i < k; i++) {
      cout << s[0];
    }
    return 0;
  }
  for (int i = s.size() - 1; i >= 1; i--) {
    string t1 = s.substr(0, i);
    string t2 = s.substr(s.size() - i, i);
    if (t1 == t2) {
      int len = s.size() - i;
      string ost = s.substr(i, len);
      string ans = s;
      for (int j = 1; j < k; j++) {
        ans += ost;
      }
      int kol = 0;
      for (int j = 0; j + s.size() <= ans.size(); j++) {
        string mr = ans.substr(j, s.size());
        if (mr == s) {
          kol++;
          if (kol == k) {
            string prt = ans.substr(0, j + s.size());
            cout << prt << endl;
            return 0;
          }
        }
      }
    }
  }
  for (int i = 1; i <= k; i++) {
    cout << s;
  }
  return 0;
}