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 long long maxN = 1e3 + 5, MOD = 998244353, INF = 1e9 + 1;
int n, k, A[maxN];
string s, t;
int main() {
  cin >> n >> k >> t;
  string aux = t + t;
  int best = 100;
  for (int i = 0; i < n - 1; i++) {
    if (t.substr(n - 1 - i) == t.substr(0, i + 1)) {
      best = i;
    }
  }
  if (best == 100) {
    best = -1;
  }
  cout << t;
  for (int i = int(0); i < int(k - 1); i++) {
    cout << t.substr(best + 1);
  }
}