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;
int main(void) {
  int n, k;
  string t;
  cin >> n >> k >> t;
  size_t len = t.length();
  ::next.resize(len + 1, 0);
  ::next[0] = -1;
  int i = 0, j = -1;
  while (i < len) {
    if (j == -1 || t[j] == t[i]) {
      i++, j++;
      ::next[i] = j;
    } else
      j = ::next[j];
  }
  cout << t;
  k -= 1;
  while (k--)
    for (size_t i = ::next[len]; i < len; i++) cout << t[i];
  return 0;
}