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>
const static long long INF = 0x3f3f3f3f3f3f3f3f;
static inline void setio(void);
int main(void) {
  setio();
  long long n, k;
  std::cin >> n >> k;
  std::string t;
  std::cin >> t;
  std::string s = t;
  long long max = 0;
  for (long long pos = 1; pos < n; ++pos) {
    std::string sub1 = t.substr(0, pos);
    std::string sub2 = s.substr(n - pos);
    if (sub1 == sub2) max = pos;
  }
  for (long long i = 1; i < k; ++i) {
    s += t.substr(max);
  }
  std::cout << s << "\n";
  return 0;
}
static inline void setio(void) {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  std::cout.precision(10);
  std::cout << std::fixed;
}