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 main() {
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  char a, b;
  a = s[0];
  b = s[s.length() - 1];
  int j = s.length() - 2;
  int i = 0;
  int maxcount = 0;
  while (j - i >= 0) {
    int k1 = j - i;
    int k = s[k1];
    int q1 = s.length() - 1;
    int q = s[q1];
    int count = 0;
    while (k1 > 0 && q == k) {
      count++;
      q1--;
      q = s[q1];
      k1--;
      k = s[k1];
    }
    if (q == k) {
      count++;
    } else {
      k1 = -1;
    }
    if (maxcount < count && k1 == 0) {
      maxcount = count;
    }
    i++;
  }
  string x = s.substr(0, s.length() - maxcount);
  string y = s.substr(s.length() - maxcount, s.length());
  for (int i = 0; i < k; i++) {
    cout << x;
  }
  cout << y;
  return 0;
}