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 long long MOD = 1e9 + 7;
int main() {
  int n, k;
  string t;
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n >> k;
  cin >> t;
  string zz = t;
  int l1 = t.length() * (k - 1);
  for (int i = 0; i < l1; i++) zz.push_back('*');
  l1 += (t.length());
  int idx = 0;
  while (k > 0) {
    string cmp = zz.substr(idx, t.length());
    int sm = 0, l2 = t.length();
    for (int i = 0; i < l2; i++)
      if (t[i] == cmp[i] || cmp[i] == '*') sm++;
    if (sm == l2) {
      k--;
      int kk = 0;
      for (int i = idx; i < idx + l2; i++) zz[i] = t[kk], kk++;
    }
    idx++;
  }
  for (int i = 0; i < l1; i++) {
    if (zz[i] == '*') break;
    cout << zz[i];
  }
  cout << "\n";
}