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 main() {
  int n, m;
  string s;
  cin >> n >> m >> s;
  unordered_set<string> map;
  string pre = "";
  for (auto i : s) {
    pre += i;
    map.insert(pre);
  }
  pre = "";
  int pos = -1;
  for (int i = n - 1; i > 0; --i) {
    pre = s[i] + pre;
    if (map.find(pre) != map.end()) {
      pos = i;
    }
  }
  string ans = "";
  if (pos == -1) {
    for (int i = 0; i < m; ++i) ans += s;
  } else {
    pre = s.substr(0, pos);
    for (int i = 0; i < m; ++i) ans += pre;
    ans += s.substr(pos);
  }
  cout << ans << endl;
}