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>
#pragma GCC optimize("O3")
using namespace std;
vector<long long> z_func(string s) {
  long long n = s.size();
  long long l = 0, r = 0;
  long long mx = 0;
  vector<long long> z(n);
  for (long long i = 1; i < n; i++) {
    if (r >= i) {
      z[i] = min(z[i - l], r - i + 1);
    }
    while (z[i] + i < n && s[z[i]] == s[z[i] + i]) z[i]++;
    if (z[i] + i - 1 > r) {
      r = z[i] + i - 1;
      l = i;
    }
  }
  return z;
}
map<string, long long> cnt;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  string r = s + "#" + s;
  vector<long long> z = z_func(r);
  long long len = 0;
  for (long long i = s.size() + 2; i < z.size(); i++) {
    if (z[i] + i == z.size()) {
      len = z[i];
      break;
    }
  }
  string t = s.substr(len, s.size() - len);
  cout << s;
  for (long long i = 2; i <= k; i++) {
    cout << t;
  }
}