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 main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  string s, t;
  long long n, k, l, ma = 0, ind;
  cin >> n >> k >> t;
  ind = t.size();
  for (long long i = 1; i < t.size(); i++) {
    long long f = 0, l = 0;
    for (long long j = i; j < t.size(); j++) {
      if (t[l] == t[j]) {
        f++;
      }
      l++;
    }
    if (f == t.size() - i && ma < f) {
      ma = f;
      ind = i;
    }
  }
  cout << t;
  for (long long i = 1; i < k; i++) {
    for (long long j = t.size() - ind; j < t.size(); j++) {
      cout << t[j];
    }
  }
}