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;
  cin >> n >> k;
  cin >> t;
  bool found = 0;
  if (n == 1) {
    for (int i = 1; i <= k; i++) cout << t;
  } else {
    string y = t;
    int index = 0;
    for (int j = 1; j < n; j++) {
      if (y[0] == t[j]) {
        found = 1;
        for (int i = 0, k = j; i < (n - j); i++, k++) {
          if (y[i] != t[k]) {
            found = 0;
            break;
          }
        }
        if (found == 1) {
          index = j;
          break;
        }
      }
    }
    if (found == 0) {
      for (int i = 1; i <= k; i++) cout << t;
    } else {
      cout << t;
      for (int i = 1; i <= (k - 1); i++) {
        for (int j = n - index; j < n; j++) cout << t[j];
      }
    }
  }
  return 0;
}