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;
vector<int> Next;
void NEXT(int m, string b);
void NEXT(int m, string b) {
  Next[0] = -1;
  int i = -1;
  int j = 0;
  while (j <= m) {
    if (i == -1 || b[i] == b[j]) {
      i++;
      j++;
      Next[j] = i;
    } else {
      i = Next[i];
    }
  }
  return;
}
int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  int n, k;
  string s, SS;
  while (cin >> n >> k) {
    Next.resize(n + 10);
    cin >> s;
    NEXT(s.size(), s);
    if (Next[s.size()] == 0) {
      SS = s;
      for (int i = 1; i < k; i++) s = s + SS;
      cout << s << endl;
      continue;
    }
    for (int i = s.size(); i >= 1; i--) {
      if (Next[i] <= Next[i - 1] || Next[i] == 0) {
        SS = s.substr(Next[s.size()], i);
        break;
      }
    }
    for (int i = 1; i < k; i++) {
      s = s + SS;
    }
    cout << s << endl;
  }
  return 0;
}