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;
string str;
int _next[1005];
void ininext() {
  _next[0] = -1;
  int i = 0, k = -1;
  while (i < str.length()) {
    if (k == -1 || str[k] == str[i]) {
      i++;
      k++;
      _next[i] = k;
    } else
      k = _next[k];
  }
}
template <typename T>
void read(T& num) {
  num = 0;
  int f = 0;
  char c = getchar();
  while (c < '0' || c > '9') {
    f |= c == '-';
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    num *= 10;
    num += c - '0';
    c = getchar();
  }
  if (f) num = -num;
}
int main(int argc, const char* argv[]) {
  int n, m;
  cin >> n >> m;
  m--;
  cin >> str;
  ininext();
  int p = _next[str.length()];
  cout << str;
  while (m--) {
    for (int i = p; i < n; i++) cout << str[i];
  }
  return 0;
}