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 n, k;
string s, t;
queue<int> q;
void init() {
  freopen(
      "a"
      ".inp",
      "r", stdin);
  freopen(
      "a"
      ".out",
      "w", stdout);
}
void Nhap() {
  scanf("%d %d", &n, &k);
  cin >> s;
}
void XuLi() {
  int tmp;
  while (k > 0) {
    if (q.empty()) {
      t.push_back(s[0]);
      for (int i = 1; i < s.size(); i++) {
        t.push_back(s[i]);
        if (s[i] == s[0]) q.push(t.size());
      }
      k--;
      continue;
    }
    tmp = q.front();
    q.pop();
    for (int j = 1; j < s.size(); j++) {
      if (tmp == (t.size())) {
        t.push_back(s[j]);
        if (s[j] == s[0]) q.push(t.size());
        tmp++;
      } else if (s[j] == t[tmp]) {
        tmp++;
        continue;
      } else {
        k++;
        break;
      }
    }
    k--;
  }
  cout << t;
}
int main() {
  Nhap();
  XuLi();
}