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, p[26];
char t[55];
bool pd(int x) {
  for (int i = 1; i <= x; ++i) {
    if (t[i] != t[n - (x - i + 1) + 1]) return 0;
  }
  return 1;
}
int main() {
  int k, l, i, j, cnt = 0;
  scanf("%d%d\n%s", &n, &k, t + 1);
  for (i = 1; i <= n; ++i)
    if (!p[t[i] - 'a']) cnt++, p[t[i] - 'a']++;
  if (cnt == 1) {
    printf("%s", t + 1);
    for (i = 1; i < k; ++i) printf("%c", t[1]);
  } else {
    for (i = n - 1; i >= 1; --i) {
      if (pd(i)) break;
    }
    l = i;
    printf("%s", t + 1);
    for (i = 1; i < k; ++i) {
      for (j = l + 1; j <= n; ++j) printf("%c", t[j]);
    }
  }
}