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;
vector<long long> edges[100005];
const long long mod = 998244353;
const long long inf = 1e15;
long long ceil_div(long long a, long long b) { return (a + b - 1) / b; }
long long power(long long a, long long b) {
  if (b == 0) return 1;
  if (a == 1) return 1;
  long long x = power(a, b / 2);
  if (b % 2 == 0)
    return x * x;
  else
    return a * x * x;
}
long long isprime(long long n) {
  for (long long i = 2; i * i <= n; i++) {
    if (n % i == 0) return 0;
  }
  return 1;
}
int main() {
  ios::sync_with_stdio(false);
  long long n, k;
  cin >> n >> k;
  string str;
  cin >> str;
  long long lps[n];
  lps[0] = 0;
  for (long long i = 1; i < n; i++) {
    long long j = lps[i - 1];
    while (j > 0 && str[i] != str[j]) j = lps[j - 1];
    if (str[i] == str[j]) j++;
    lps[i] = j;
  }
  long long x = n - lps[n - 1];
  string res = str.substr(0, x);
  string ans = "";
  while (k > 1) {
    ans += res;
    k--;
  }
  ans += str;
  cout << ans << '\n';
}