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 long long INF = 1e9;
const int N = 5e3 + 5;
const int MOD = 1e9 + 7;
const double EPS = 1e-8;
const double PI = acos(-1);
long long n, t;
string s;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL), cout.tie(NULL);
  cin >> n >> t;
  cin >> s;
  long long k = -1;
  for (int r = n - 1; r > 0; r--) {
    if (s[r] == s[0]) {
      bool ok = true;
      for (int i = 0; i + r < n; i++) {
        if (s[i + r] != s[i]) {
          ok = false;
          break;
        }
      }
      if (ok) {
        k = r;
      }
    }
  }
  if (~k) {
    string l = "", r = "";
    for (int i = 0; i < n - k; i++) {
      l += s[i];
    }
    for (int i = n - k; i < n; i++) {
      r += s[i];
    }
    cout << l;
    while (t--) cout << r;
  } else
    while (t--) cout << s;
  cout << '\n';
}