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 MOD = 1000000007;
const long long INF = 1e18;
const int MX = 100001;
int findPos(string second) {
  for (int i = 1; i < (second.length()); i++) {
    if (second.substr(i, second.length() - i) ==
        second.substr(0, second.length() - i)) {
      return i;
    }
  }
  return second.length();
}
int main() {
  int n, k;
  string second;
  cin >> n >> k >> second;
  int pos = findPos(second);
  string ans = "";
  for (int i = 0; i < (k); i++) {
    if (i == 0) {
      ans += second;
    } else {
      ans += second.substr(second.length() - pos, pos);
    }
  }
  cout << ans;
}