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;
  string t, ans = "\0";
  cin >> n >> k;
  cin >> t;
  if (n == 1) {
    while (k--) {
      ans += t;
    }
  } else {
    int i = 1, j = 0;
    int len = t.length();
    while (i < len) {
      j = 0;
      if (t[0] == t[i]) {
        while (t[j] == t[i]) {
          i += 1;
          j += 1;
          if (i == len) {
            break;
          }
        }
        if (i != len) {
          j = 0;
          if ((t[i - 1] == t[0]) && (t[i] == t[1])) {
            i -= 1;
          }
        }
      } else {
        i += 1;
      }
    }
    string added = t.substr(j, n);
    ans += t;
    while (--k) {
      ans += added;
    }
  }
  cout << ans << endl;
  return 0;
}