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;
string a[51], b[51];
char s[2002];
int n, k;
int main() {
  scanf("%d%d", &n, &k);
  scanf("%s", s);
  for (int i = 0; i < n; i++) a[i + 1] = a[i] + s[i];
  for (int i = n - 1; i >= 0; i--) b[i + 1] = s[i] + b[i + 2];
  int ans = 0;
  for (int i = n - 1; i >= 1; i--)
    if (a[i] == b[n + 1 - i]) ans = max(i, ans);
  for (int j = 1; j < k; j++)
    for (int i = 1; i <= n - ans; i++) cout << s[i - 1];
  for (int i = 1; i <= n; i++) cout << s[i - 1];
  return 0;
}