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 = 100050;
char a[maxn];
int nxt[maxn];
int m;
void getnxt() {
  int j = 0;
  int i = 1;
  nxt[0] = 0;
  while (i < m) {
    if (a[i] == a[j]) {
      nxt[i++] = ++j;
    } else if (!j) {
      i++;
    } else {
      j = nxt[j - 1];
    }
  }
}
int main() {
  int n, k;
  cin >> n >> k;
  cin >> a;
  m = strlen(a);
  getnxt();
  cout << a;
  int id = nxt[m - 1];
  for (int i = 2; i <= k; i++) {
    for (int j = id; j < m; j++) {
      cout << a[j];
    }
  }
  cout << endl;
  return 0;
}