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 firstLine = readline();
var n = firstLine.split(" ")[0];
var k = firstLine.split(" ")[1];
var string = readline();

print(output(string, k, n))

function output(string, k, n) {
    var p = n - 1;
    var l = 0;
    var ans = 0;
    for (var i = p - 1; i >= 0; i--) {
        if (ans === 0) {
            for (var j = i; j >= 0; j--) {
                if (string[j] === string[p]) {
                    p--;
                    l++;
                    if (j === 0) {
                        ans = l;
                    }
                } else {
                    p = n - 1;
                    l = 0;
                    break;
                }
            }
        } else {
            break;
        }
    }

    for (var i = 1; i <= k - 1; i++) {
        for (var j = l; j < n; j++) {
            string += string[j];
        }
    }
    return string;
}