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;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  template <class c>
  debug& operator<<(const c&) {
    return *this;
  }
};
void solve() {
  int n, k;
  char s[500];
  scanf("%d %d %s", &n, &k, s);
  int ans = 0;
  for (int i = 1; i <= n - 1; i++) {
    int flag = 0;
    for (int j = 0; j < i; j++) {
      if (s[j] != s[n - i + j]) flag++;
    }
    if (flag == 0) ans = i;
  }
  string st = s;
  st.erase(0, ans);
  printf("%s", s);
  for (int i = 1; i < k; i++) printf("%s", st.c_str());
  puts("");
}
int main() { solve(); }