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;
const int maxn = 1000000;
int n, k;
string s;
int main(void) {
  cin >> n >> k;
  cin >> s;
  int len = s.size();
  string str1, str2;
  int res = 0;
  for (int i = len - 2; i >= 0; i--) {
    str1 = "", str2 = "";
    for (int j = 0; j <= i; j++) str1 += s[j];
    for (int j = len - 1; j >= len - i - 1; j--) str2 += s[j];
    reverse(str2.begin(), str2.end());
    int j;
    for (j = 0; j < (int)str1.size(); j++) {
      if (str1[j] != str2[j]) break;
    }
    if (j == (int)str1.size()) {
      res = j;
      break;
    }
  }
  cout << s;
  string str;
  if (res == 0) {
    for (int i = 1; i < k; i++) cout << s;
  } else {
    for (int i = (int)str1.size(); i < len; i++) str += s[i];
    for (int i = 1; i < k; i++) {
      cout << str;
    }
  }
  cout << endl;
  return 0;
}