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 int maxn = 105;
long long int n, ans;
long long int a[maxn], b[maxn], p[maxn];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int t;
  t = 1;
  while (t--) {
    long long int n, k;
    cin >> n >> k;
    string s;
    cin >> s;
    long long int f = 1;
    for (long long int i = 0; i < (long long int)(n - 1); i++) {
      if (s[i] != s[i + 1]) f = 0;
    }
    if (f == 1) {
      cout << s;
      k--;
      while (k--) cout << s[0];
    } else {
      string q;
      long long int p = 0;
      for (int i = n - 2; i >= 0; i--) {
        if (s.substr(0, i + 1) == s.substr(n - 1 - i, i + 1)) {
          q = s.substr(i + 1);
          break;
        }
      }
      if (q.length() == 0) q = s;
      cout << s;
      for (long long int i = 0; i < (long long int)(k - 1); i++) {
        cout << q;
      }
    }
  }
}