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 a[2510];
int ne[2510];
void get(int x) {
  int i, j;
  i = 0;
  j = -1;
  ne[0] = -1;
  while (i < x) {
    if (a[i] == a[j] || j == -1) {
      i++;
      j++;
      ne[i] = j;
    } else
      j = ne[j];
  }
}
int main() {
  int i, j, k, n, m;
  scanf("%d%d", &n, &m);
  scanf("%s", a);
  get(n);
  k = n;
  for (j = 2; j <= m; j++) {
    for (i = ne[n]; i < n; i++) a[k++] = a[i];
  }
  a[k] = '\0';
  printf("%s\n", a);
  return 0;
}