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;
const int inf = 0x3f3f3f3f;
const int mod = 1e9 + 7;
int n, k;
string str;
int main() {
  cin >> n >> k >> str;
  int mx = 0;
  for (int i = 1; i < n; i++) {
    int gd = 1;
    for (int j = 0; j < i; j++)
      if (str[j] != str[n - i + j]) gd = 0;
    if (gd) mx = i;
  }
  cout << str;
  for (int i = 2; i <= k; i++)
    for (int j = mx; j < n; j++) cout << str[j];
  return 0;
}