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>
double PI = 3.14159265;
long long int mod = 1e9 + 9;
using namespace std;
bool checkprime(long long int n) {
  for (long long int i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}
int main() {
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  map<char, int> m;
  for (int i = 0; i < n; i++) {
    m[s[i]]++;
  }
  if (m.size() == 1) {
    for (int i = 1; i <= k - 1; i++) {
      s += s[0];
    }
    cout << s << endl;
  } else {
    string t, ans, op = "";
    for (int i = 0; i < n; i++) {
      t = s.substr(i);
      ans = s + t;
      bool f = true;
      int k = 0;
      for (int j = ans.size() - n; j < ans.size(); j++) {
        if (s[k++] != ans[j]) {
          f = false;
        }
      }
      if (f) {
        op = t;
      }
    }
    for (int i = 1; i <= k - 1; i++) {
      s += op;
    }
    cout << s << endl;
  }
}