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;
char s[105];
int nt[105];
char c[105];
int k, j, n;
int pnt(char s[], int len) {
  int i, j;
  i = 0;
  j = -1;
  while (i < len) {
    if (j == -1 || s[i] == s[j]) {
      i++;
      j++;
      nt[i] = j;
    } else {
      j = nt[j];
    }
  }
  return nt[len];
}
int main() {
  int len, t;
  nt[0] = -1;
  cin >> n >> k;
  cin >> s;
  t = pnt(s, n);
  for (int i = 0; i < n - t; i++) {
    c[i] = s[i];
  }
  for (int i = 1; i <= k; i++) {
    cout << c;
  }
  for (int i = n - t; i < n; i++) {
    cout << s[i];
  }
  return 0;
}