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;
inline long long read() {
  long long kk = 0, f = 1;
  char cc = getchar();
  while (cc < '0' || cc > '9') {
    if (cc == '-') f = -1;
    cc = getchar();
  }
  while (cc >= '0' && cc <= '9') {
    kk = (kk << 1) + (kk << 3) + cc - '0';
    cc = getchar();
  }
  return kk * f;
}
int n, k;
int mnext[55];
char ss[50005], s1[55];
void cnext() {
  int i, j;
  mnext[0] = -1;
  for (i = 1; i < n; ++i) {
    j = mnext[i - 1];
    while (j > -1 && s1[j + 1] != s1[i]) j = mnext[j];
    if (s1[j + 1] == s1[i])
      mnext[i] = j + 1;
    else
      mnext[i] = -1;
  }
}
int T;
int main() {
  n = read();
  k = read();
  cin >> s1;
  cnext();
  T = n - mnext[n - 1] - 1;
  for (int i = 1; i <= k; ++i)
    for (int j = 0; j < T; ++j) cout << s1[j];
  for (int j = T; j < n; ++j) cout << s1[j];
}