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;
string t;
int main() {
  cin >> n >> k;
  cin >> t;
  string s;
  int* nxt = new int[n];
  nxt[0] = -1;
  int i, j;
  for (i = 0; i < n; i++) {
    j = i - 1;
    while (j >= 0 && t[nxt[j] + 1] != t[i]) j = nxt[j];
    if (j < 0)
      nxt[i] = -1;
    else
      nxt[i] = nxt[j] + 1;
  }
  string sub = t.substr(nxt[n - 1] + 1, n);
  for (int i = 0; i < k - 1; i++) t += sub;
  cout << t;
  return 0;
}