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 >> t;
  bool equal = true;
  for (int i = 1; i < n; i++)
    if (t[i] != t[i - 1]) equal = false;
  if (equal) {
    for (int i = 1; i < k; i++) t.push_back(t[0]);
    cout << t << endl;
    return 0;
  }
  int sub_l = n - 1;
  for (; sub_l > 0; sub_l--) {
    bool ok = true;
    for (int i = 0; i < sub_l; i++) {
      if (t[i] != t[n - sub_l + i]) ok = false;
    }
    if (ok) break;
  }
  if (sub_l == 0) {
    for (int i = 0; i < k; i++)
      for (int j = 0; j < n; j++) cout << t[j];
    cout << endl;
  } else {
    for (int i = 0; i < k - 1; i++) {
      for (int j = 0; j < n - sub_l; j++) cout << t[j];
    }
    cout << t << endl;
  }
}