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 INF = 1e9;
const long long INFF = 1e18;
const int MAXN = 510;
const int MOD = 1e9 + 7;
const double PI = acos(-1.0);
const double INFD = 1E9;
const double EPS = 1e-9;
bool cek(string s, int pos) {
  int n = s.length();
  int x = n - 1 - pos;
  for (int i = 0; i <= pos; i++) {
    if (s[i] != s[x]) return false;
    ++x;
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  string tambah;
  for (int i = n - 2; i >= 0; i--) {
    if (cek(s, i)) {
      for (int j = i + 1; j < n; j++) tambah += s[j];
      break;
    }
  }
  if (tambah == "") tambah = s;
  for (int i = 1; i < k; i++) s += tambah;
  cout << s << endl;
  return 0;
}