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;
const int N = 1e5 + 10;
const int mod = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const double EXP = 1e-9;
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n, k;
  string s;
  cin >> n >> k >> s;
  int idx = -1;
  bool flag = 0;
  for (int i = 1; i < n; ++i) {
    if (s[i] == s[0]) {
      int j = 0;
      for (j = i + 1; j < n; ++j) {
        if (s[j] != s[j - i]) break;
      }
      if (j == n) {
        idx = i;
        break;
      }
    }
  }
  for (int i = 0; i < n - 1; ++i) {
    if (s[i] != s[i + 1]) {
      flag = 1;
      break;
    }
  }
  if (flag == 0) {
    for (int i = 0; i < n + k - 1; ++i) cout << s[0];
    cout << '\n';
  } else if (idx == -1) {
    for (int i = 0; i < k; ++i) cout << s;
    cout << '\n';
  } else {
    for (int i = 0; i < k; ++i) {
      for (int j = 0; j < idx; ++j) cout << s[j];
    }
    for (int i = idx; i < n; ++i) cout << s[i];
    cout << '\n';
  }
  return 0;
}