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, e = "", st = "";
  cin >> s;
  int c = 0, br = 0, res = 0, x = 0;
  for (int i = 1; i < s.length(); i++) {
    int j = i;
    int idx = 0;
    int tmp = 0;
    while (s[j] == s[idx] && j < s.length()) tmp++, j++, idx++;
    if (j == s.length()) res = max(res, tmp);
  }
  for (int i = 0; i < n; i++) {
    if (i < res) {
      st += s[i];
    } else {
      e += s[i];
    }
  }
  string pp = "";
  for (int i = 0; i <= k; i++) {
    if (i == 0) {
      pp += st;
    } else
      pp += e;
  }
  cout << pp << endl;
}