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 JAVA):

Solution:

var nk = readline();
var t = readline();

var n = nk.split(" ")[0];
var k = nk.split(" ")[1];

var equal = "";
for (var i = 0; i < t.length - 1; i ++) {
    var firstSub = t.substring(0, i + 1);
    var secondSub = t.substring(t.length - i - 1, t.length);
    
    if (firstSub === secondSub) {
      equal = firstSub;
    }
  }

var result = t;
for (var i = 1; i < k; i ++) {
    if (equal !== "") {
        result += t.substring(equal.length, t.length);
    } else {
        result += t;
    }
}

write(result);