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 M = 1e9 + 7;
int n, k;
string t, ans;
bool ch(int x) {
  string s1, s2;
  for (int i = 0; i < x; ++i) s1 += t[i];
  for (int i = n - x; i < n; ++i) s2 += t[i];
  return s1 == s2;
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  cin >> n >> k;
  cin >> t;
  int z = 0;
  string t2;
  ans = t;
  for (int i = 1; i <= n - 1; ++i) {
    if (ch(i)) z = i;
  }
  for (int i = z; i < n; ++i) t2 += t[i];
  while (--k > 0) ans += t2;
  cout << ans << "\n";
}