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, k;
  string s;
  cin >> n >> k >> s;
  string res = s, add = s;
  k--;
  for (int i = 0; i < n - 1; i++) {
    string a = "", b = "";
    for (int j = 0; j <= i; j++) a += s[j];
    for (int j = n - i - 1; j < n; j++) {
      b += s[j];
    }
    if (a == b) {
      add = "";
      for (int j = i + 1; j < n; j++) add += s[j];
    }
  }
  while (k--) {
    res += add;
  }
  cout << res;
  return 0;
}