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;
long long a;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long a, b;
  cin >> a >> b;
  string s;
  cin >> s;
  cout << s;
  b--;
  long long i;
  long long pos = 0;
  string s2;
  long long f = 0;
  for (i = 0; i <= a - 1; i++) {
    string s1 = s.substr(0, i + 1);
    for (long long j = 0; j < a; j++) {
      s2 = s.substr(j, a);
      if (s1 == s2 && i != (a - 1)) {
        pos = i;
        f = 1;
      }
    }
  }
  if (f == 1) pos++;
  for (long long j = 0; j < b; j++) {
    for (long long k = pos; k < a; k++) cout << s[k];
  }
}