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 = 100020;
const int maxk = 620;
const int MOd = 1e9 + 7;
const int K = 300;
int a, b;
int fail[maxn];
char ar[maxn];
int main() {
  scanf("%d %d", &a, &b);
  for (int i = 1, p = 0; i <= a; i++) {
    scanf(" %c", &ar[i]);
    while (p > 0 && ar[i] != ar[p + 1]) p = fail[p];
    if (p + 1 < i && ar[i] == ar[p + 1]) p++;
    fail[i] = p;
  }
  int ans = b;
  for (int i = 1; i <= fail[a]; i++) printf("%c", ar[i]);
  for (int i = 1; i <= ans; i++) {
    for (int j = fail[a] + 1; j <= a; j++) printf("%c", ar[j]);
  }
  printf("\n");
  return 0;
}