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 = 100;
int n, k;
char s[maxN];
int main() {
  cin >> n >> k >> (s + 1);
  int idx;
  for (idx = 2; idx <= n; ++idx) {
    bool ok = 1;
    for (int i = idx, j = 1; i <= n && j <= n; ++i, ++j) {
      ok &= (s[i] == s[j]);
    }
    if (ok) {
      break;
    }
  }
  string ans;
  for (int i = 1; i <= n; ++i) {
    ans += s[i];
  }
  while (--k) {
    for (int i = n - idx + 2; i <= n; ++i) {
      ans += s[i];
    }
  }
  cout << ans;
  return 0;
}