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;
using namespace std;
const int N = 1e4 + 5;
char s[N];
int Next[N];
int l, c;
void kmp(char *s, int *next) {
  int len = strlen(s);
  next[0] = -1;
  int k = -1;
  for (int q = 1; q < len; q++) {
    while (k > -1 && s[k + 1] != s[q]) k = next[k];
    if (s[k + 1] == s[q]) k++;
    next[q] = k;
  }
}
int main() {
  std::ios::sync_with_stdio(false);
  cin >> l >> c;
  cin >> s;
  kmp(s, Next);
  int len = l - Next[l - 1] - 1;
  for (int i = 0; i < c; i++) {
    for (int j = 0; j < len; j++) cout << s[j];
  }
  for (int i = len; i < l; i++) cout << s[i];
  return 0;
}