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 PYTHON3):

Solution:
# -*- coding: utf-8 -*-

n, k = map(int, input().split())
t = input()

cnt = 1
pos = 1
ans = t
while (cnt < k):
    if pos >= len(ans):
        ans += t
        cnt += 1
    else:
        ok = True
        l = 0
        for i in range(len(t)):
            if pos + i >= len(ans):
                break
            l += 1
            if ans[pos + i] != t[i]:
                ok = False
        if ok:
            ans += t[l:]
            cnt += 1
    pos += 1
print(ans)