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;
char s[10000], ne[1000];
void kmp(int n) {
  ne[0] = -1;
  for (int i = 1; i < n; ++i) {
    int j = ne[i - 1];
    while (s[i] != s[j + 1] && j >= 0) j = ne[j];
    if (s[i] == s[j + 1])
      ne[i] = j + 1;
    else
      ne[i] = -1;
  }
}
char t[10000];
int main() {
  int n, k;
  scanf("%d%d%s", &n, &k, s);
  kmp(n);
  int p = ne[n - 1] + 1;
  for (int i = 0; p < n; ++p, ++i) t[i] = s[p];
  for (int i = 1; i < k; ++i) strcat(s, t);
  printf("%s", s);
  return 0;
}