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 a[52];
int kmp[52];
int main() {
  int j, i, n, m;
  scanf("%d%d%s", &n, &m, a + 1);
  j = 0;
  for (i = 2; i <= n; ++i) {
    while (j && a[i] != a[j + 1]) j = kmp[j];
    if (a[j + 1] == a[i]) j++;
    kmp[i] = j;
  }
  for (i = 1; i <= kmp[n]; ++i) printf("%c", a[i]);
  for (i = 1; i <= m; ++i)
    for (j = kmp[n] + 1; j <= n; ++j) printf("%c", a[j]);
  return 0;
}