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;
using ll = long long;
using Lll = list<ll>;
using Vll = vector<ll>;
using Vd = vector<double>;
using Matll = vector<Vll>;
double mod = 1e20;
ll ms = 1123456789;
int main() {
  ll n, k;
  string s, t;
  cin >> n >> k >> s;
  for (ll i = 0; i < n - 1; i += 1) {
    string a(s.begin() + n - i - 1, s.end()), b(s.begin(), s.begin() + i + 1);
    if (a == b) t = a;
  }
  string c(s.begin(), s.begin() + s.size() - t.size());
  if (c.size() == 0) {
    c.push_back(s[0]);
    t.pop_back();
  }
  for (ll i = 0; i < k; i += 1) {
    cout << c;
  }
  cout << t << endl;
}