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 argc, char** argv) {
  int n, k;
  cin >> n >> k;
  string str;
  cin >> str;
  if (k == 1) {
    cout << str << endl;
    return 0;
  }
  if (n == 1) {
    for (int i = 0; i < k; i++) {
      cout << str;
    }
    cout << endl;
    return 0;
  }
  string ans = str;
  int index = 0;
  string a;
  int maxIndex = 0;
  for (int i = 1, j = 0; i < ans.length() && j < str.length(); i++) {
    bool x = true;
    int J = 0;
    for (int k = i; k < ans.length(); k++, J++) {
      if (str[J] != ans[k]) {
        x = false;
        break;
      }
    }
    if (x) {
      index = J;
      if (index > maxIndex) maxIndex = index;
    }
  }
  for (int i = maxIndex; i < str.length(); i++) a = a + str[i];
  cout << ans;
  for (int i = 2; i <= k; i++) cout << a;
  cout << endl;
  return 0;
}