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;
struct sp {
  char s;
  long m;
};
sp w[60];
long k, n;
void inic() {
  for (long i = 0; i < 60; i++) {
    w[i].m = 0;
    w[i].s = ' ';
  }
  k = 0;
  n = 0;
};
void kmp() {
  long mark = 0, pos = 2;
  while (pos <= n) {
    if (w[pos].s == w[mark + 1].s) {
      mark++;
      w[pos].m = mark;
      pos++;
    } else if (mark == 0) {
      w[pos].m = mark;
      pos++;
    } else
      mark = w[mark].m;
  }
};
void vivod() {
  for (long i1 = 1; i1 <= k; i1++) {
    for (long i2 = 1; i2 <= (n - w[n].m); i2++) {
      cout << w[i2].s;
    }
  }
  for (long i = (n - w[n].m + 1); i <= n; i++) {
    cout << w[i].s;
  }
};
int main() {
  inic();
  cin >> n >> k;
  for (long i = 1; i <= n; i++) {
    cin >> w[i].s;
  }
  kmp();
  vivod();
  return 0;
}