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 Next[105], n, m;
char s[105];
int len;
void getnext() {
  int i = 0, j = -1;
  Next[i] = j;
  while (i < len) {
    if (j == -1 || s[i] == s[j])
      Next[++i] = ++j;
    else
      j = Next[j];
  }
}
int main() {
  scanf("%d%d%s", &n, &m, s);
  len = strlen(s);
  int num = 1;
  printf("%s", s);
  getnext();
  while (num < m) {
    int i = Next[len];
    while (i < len) printf("%c", s[i++]);
    num++;
  }
}