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;
int n, nr;
char s[55];
int main() {
  cin >> n >> nr;
  cin.get();
  cin >> s;
  bool sirNemonoton = true;
  for (int i = 1; i <= n - 1; i++)
    if (s[i] != s[i - 1]) {
      sirNemonoton = false;
      break;
    }
  if (sirNemonoton == true) {
    cout << s;
    for (int i = 2; i <= nr; i++) cout << s[0];
    return 0;
  }
  int bigPref = 0;
  for (int i = 1; i <= n - 1; i++) {
    bool ok = true;
    int posSufBegin = n - i;
    for (int j = 0; j <= i - 1; j++) {
      if (s[j] != s[posSufBegin + j]) {
        ok = false;
        break;
      }
    }
    if (ok == true) bigPref = i;
  }
  int addForNextSubstring = n - bigPref;
  cout << s;
  for (int i = 2; i <= nr; i++) {
    for (int j = bigPref; j <= n - 1; j++) cout << s[j];
  }
  return 0;
}