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>
#pragma GCC optimize("O3")
using namespace std;
int n, k;
string s;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
  cin >> n >> k;
  cin >> s;
  int ss = 0;
  for (int i = 1; i < s.size(); ++i) {
    bool gg = 1;
    for (int j = 0; j < i; ++j)
      if (s[j] != s[s.size() - (i - j)]) gg = 0;
    if (gg) ss = i;
  }
  cout << s;
  for (int i = 2; i <= k; ++i)
    for (int j = ss; j < s.size(); ++j) cout << s[j];
  return 0;
}