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 = 1e18;
const int inf = 1e9, dx[] = {0, 0, 1, -1, 1, -1, 1, -1},
          dy[] = {1, -1, 0, 0, 1, 1, -1, -1}, MOD = 1e9 + 7;
long double eps = 1e-7, pi = acos(-1);
int n, k, cnt;
string t, s;
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> k >> t;
  for (int i = 1; i < n; i++)
    if (t.substr(0, i) == t.substr(n - i, i)) cnt = i;
  cout << t;
  for (int i = 1; i < k; i++) cout << t.substr(cnt, n - cnt);
  return 0;
}