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 maxn = 1e5 + 10;
int n, k;
char s[maxn];
char tar[maxn];
int num[maxn];
bool judge(int x) {
  for (int i = 0; i < n; i++) {
    if (tar[x + i] != s[i]) return false;
  }
  return true;
}
bool judge2(int x, int l) {
  for (int i = x; i < n && i < x + l; i++)
    if (s[i] != s[i - x]) return false;
  return true;
}
void solve() {
  int sz = n;
  for (int l = 1; l < n; l++) {
    bool flag = true;
    for (int i = l; i < n; i += l)
      if (!judge2(i, l)) flag = false;
    if (flag) {
      sz = l;
      break;
    }
  }
  for (int i = 0; i < 3000; i++) tar[i] = s[i % sz];
  int count = 0;
  for (int i = 0; i < 3000 - n; i++) {
    if (judge(i)) {
      count++;
      if (count == k) {
        tar[i + n] = 0;
        cout << tar << endl;
        return;
      }
    }
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> n >> k >> s;
  solve();
  return 0;
}