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;
int n, k;
bool ff;
char t[55];
int getit(int x) {
  if (n % 2 != 0) {
    if (x == n / 2 + 1)
      return x;
    else if (x > n / 2 + 1)
      return x - n / 2 - 1;
    else
      return n + 1 - x;
  } else {
    if (x > n / 2)
      return x - n / 2;
    else
      return n + 1 - x;
  }
}
int main() {
  int i, j;
  int x = 0, tm;
  scanf("%d%d", &n, &k);
  scanf("%s", t + 1);
  ff = 0;
  for (i = 2; i <= n; i++)
    if (t[i] != t[i - 1]) {
      ff = 1;
      break;
    }
  if (!ff) {
    for (i = 1; i <= n; i++) cout << t[1];
    for (i = 1; i < k; i++) cout << t[1];
    cout << endl;
    return 0;
  }
  tm = n;
  bool flag;
  for (i = 1; i < n; i++) {
    flag = 1;
    for (j = 1; j <= i; j++) {
      if (t[j] != t[tm + j - 1]) {
        flag = 0;
        break;
      }
    }
    if (flag) x = max(x, i);
    tm--;
  }
  for (i = 1; i <= n; i++) {
    cout << t[i];
  }
  for (i = 1; i < k; i++) {
    for (j = x + 1; j <= n; j++) cout << t[j];
  }
  return 0;
}