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;
string s, dummy;
int n, k;
int main() {
  cin >> n >> k;
  cin >> s;
  int i = 1, p, target = -1, j;
  int len = INT_MAX;
  while (i < s.length()) {
    if (s[0] == s[i]) {
      p = 0;
      j = i;
      i++;
      while (1) {
        if (j == s.length()) {
          break;
        }
        if (s[p] == s[j]) {
          p++;
          j++;
        } else {
          break;
        }
      }
      if (j == s.length()) {
        if (len > (s.length() - p)) {
          len = (s.length() - p);
          target = p;
        }
      } else {
      }
    } else {
      i++;
    }
  }
  if (target == -1) {
    dummy = s;
    k -= 1;
    while (k > 0) {
      s += dummy;
      k -= 1;
    }
  } else {
    dummy = s.substr(target, (s.length() - target));
    k -= 1;
    while (k > 0) {
      s += dummy;
      k -= 1;
    }
  }
  cout << s << endl;
  return 0;
}