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 next1[100];
void getNext(char p[]) {
  int len = strlen(p);
  next1[0] = 0;
  int i = 0, j = 0;
  for (j = 1; j < len; j++) {
    while (p[i] != p[j] && i > 0) i = next1[i - 1];
    if (p[i] == p[j]) {
      i++;
      next1[j] = i;
    } else
      next1[j] = 0;
  }
}
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  char p[100];
  cin >> p;
  int len = strlen(p);
  getNext(p);
  int kk = next1[len - 1];
  for (int i = 0; i < kk; i++) {
    printf("%c", p[i]);
  }
  while (k--) {
    for (int i = kk; i < len; i++) printf("%c", p[i]);
  }
  cout << endl;
  return 0;
}