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() {
  long long n, k;
  cin >> n >> k;
  string str;
  cin >> str;
  int overlap = -1;
  int max = -1;
  for (int i = 1; i < n; ++i) {
    if (str[i] == str[0]) {
      int j = 0;
      for (j = 0; i + j < n; ++j) {
        if (str[i + j] == str[j]) continue;
        break;
      }
      if (i + j == n && j > max) {
        overlap = i;
        max = j;
      }
    }
  }
  string firstHalf = "";
  string secondHalf = str;
  if (overlap != -1) {
    firstHalf = str.substr(0, overlap);
    secondHalf = str.substr(overlap);
    long long secondLen = secondHalf.length();
    firstHalf = str.substr(0, secondLen);
    secondHalf = str.substr(secondLen);
  }
  for (int x = 0; x < k; ++x) {
    if (x == 0)
      cout << str;
    else
      cout << secondHalf;
  }
  cout << endl;
  return 0;
}