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, k, l, s, t;
char p[100];
char ans[10005];
int main() {
  cin >> l >> t;
  getchar();
  gets(p);
  s = l;
  for (int i = 0; i < l; i++) ans[i] = p[i];
  for (int i = 2; i <= t; i++) {
    int flag = 0, u1 = s;
    for (int j = 1; j < s; j++) {
      int fi = -1, opt = 0;
      for (int u = l - (s - j); u < l; u++) {
        if (ans[u] != p[++fi]) {
          opt = 1;
          break;
        }
      }
      if (!opt) {
        flag = 1;
        u1 = j;
        break;
      }
    }
    for (int j = s - u1; j < s; j++) ans[l++] = p[j];
  }
  puts(ans);
  return 0;
}