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;
const int N = 55;
char s[N], p[N];
int ne[N];
int main() {
  int n, k;
  scanf("%d%d%s", &n, &k, p + 1);
  for (int i = 2, j = 0; i <= n; i++) {
    while (j && p[j + 1] != p[i]) j = ne[j];
    if (p[j + 1] == p[i]) j++;
    ne[i] = j;
  }
  for (int i = 1; i <= n; i++) printf("%c", p[i]);
  for (int i = 1; i < k; i++)
    for (int j = ne[n] + 1; j <= n; j++) printf("%c", p[j]);
  return 0;
}