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 = 1e6 + 5;
int arr[maxn];
void solve() {
  int n, k;
  scanf("%d", &n);
  scanf("%d", &k);
  string str;
  cin >> str;
  int start = 0, end = n - 1;
  for (int i = 1; i <= n - 1; i++) {
    int suff = i;
    int pre = 0;
    while (str[pre] == str[suff]) {
      pre++;
      suff++;
    }
    if (suff == n) {
      start = n - i;
      break;
    }
  }
  k--;
  cout << str;
  while (k--) {
    for (int i = start; i <= end; i++) {
      cout << str[i];
    }
  }
  cout << endl;
}
int main() {
  int t = 1;
  while (t--) {
    solve();
  }
}