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 str, s, s1;
  string sub1, sub2, t;
  scanf("%d", &n);
  scanf("%d", &m);
  cin >> str;
  t = str;
  s1 = str;
  int cnt = 0;
  for (int i = 1, j = n - 1; i < n; i++, j--) {
    sub1 = str.substr(0, i);
    sub2 = str.substr(j, i);
    if (sub1 == sub2) {
      cnt = sub1.size();
    }
    sub1.clear();
    sub2.clear();
  }
  for (int i = 0; i < cnt; i++) {
    s1.erase(0, 1);
  }
  for (int i = 1; i < m; i++) {
    t = t + s1;
  }
  cout << t << endl;
  return 0;
}