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 n, k, l;
char tt[61];
int nt[61];
void maken() {
  int now = 0;
  for (int i = 2; i <= l; i++) {
    while (now > 0 && tt[now + 1] != tt[i]) now = nt[now];
    if (tt[now + 1] == tt[i]) now++;
    nt[i] = now;
  }
}
int main() {
  scanf("%d%d", &n, &k);
  scanf("%s", tt + 1);
  printf("%s", tt + 1);
  if (k == 1) {
    return 0;
  }
  l = strlen(tt + 1);
  maken();
  for (int i = 1; i < k; i++) {
    for (int j = nt[l] + 1; j <= l; j++) printf("%c", tt[j]);
  }
  return 0;
}