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;
char s[55];
int read() {
  char c = getchar();
  int x = 0, f = 1;
  while (c < '0' || c > '9') {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    x = x * 10 + c - '0';
    c = getchar();
  }
  return x * f;
}
int main() {
  int n = read(), k = read();
  scanf("%s", s);
  for (int i = n - 2; i >= -1; i--) {
    bool f = true;
    for (int j = 0; j <= i; j++) {
      if (s[j] != s[n - 1 - i + j]) {
        f = false;
      }
    }
    if (f) {
      for (int j = 1; j < k; j++) {
        for (int l = 0; l < n - i - 1; l++) {
          printf("%c", s[l]);
        }
      }
      for (int j = 0; j < n; j++) printf("%c", s[j]);
      printf("\n");
      exit(0);
    }
  }
  return 0;
}