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 n, k, i;
string t, tt, t1, t2;
int main() {
  cin >> n >> k;
  cin >> t;
  t1 = t2 = t;
  for (i = 1; i <= n; i++) {
    tt = t2[t2.end() - 1 - t2.begin()] + tt;
    t1.erase(t1.begin());
    t2.erase(t2.end() - 1);
    if (t1 == t2) break;
  }
  cout << t;
  for (i = 1; i < k; i++) cout << tt;
  cout << '\n';
  return 0;
}