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 nxt[55], l, k;
string a;
void getnext(string s) {
  int j = -1;
  nxt[0] = -1;
  for (int i = 1; i < l; i++) {
    while (j != -1 && s[j + 1] != s[i]) j = nxt[j];
    if (s[j + 1] == s[i]) j++;
    nxt[i] = j;
  }
  return;
}
int main() {
  scanf("%d%d", &l, &k);
  cin >> a;
  getnext(a);
  int len = l - 1 - nxt[l - 1];
  for (int i = 1; i <= k; i++)
    for (int j = 0; j < len; j++) cout << a[j];
  for (int i = len; i < l; i++) cout << a[i];
  return 0;
}