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 long long int MOD = 1e9 + 7, INF = 0x3F3F3F3F3F3F3F3F;
const int inf = 0x3F3F3F3F;
int kmp(string s) {
  int arr[s.size() + 1];
  arr[0] = 0;
  int i = 1;
  int j = 0;
  while (i < s.size()) {
    if (s[i] == s[j]) {
      j++;
      arr[i] = j;
      i++;
    } else {
      if (j != 0) {
        j = arr[j - 1];
      } else {
        arr[i] = 0;
        i++;
      }
    }
  }
  return arr[s.size() - 1];
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  cout << s;
  int i = kmp(s);
  k -= 1;
  string temp = s.substr(i, s.size() - i);
  while (k--) {
    cout << temp;
  }
  cout << endl;
  return 0;
}