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 mod = 998244353;
const long long inf = 1000000000000000000;
long long f[110];
int main() {
  long long n, k;
  string s;
  cin >> n >> k >> s;
  long long ma = 0;
  for (int i = 1; i < n; i++) {
    string a, b;
    a = s.substr(0, i);
    b = s.substr(n - i, i);
    if (a == b) ma = i;
  }
  string a = s.substr(0, ma), b = s.substr(ma, n - ma);
  cout << a;
  while (k--) cout << b;
  cout << endl;
  return 0;
}