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:
n, K = map(int, input().split())
string = input()
idx = []
first = string[0]
for i in range(len(string)):
    if first == string[i]:
        idx.append(i)

tmp = False
k = 0
for i in idx:
    if i == 0:
        continue


    k = 0
    for j in range(i, len(string)):
        if string[k] != string[j]:
            break

        k += 1
    else:
        tmp = True
        break

import sys
# k += 1
if tmp:
    s = string[k:]
    sys.stdout.write(string)
    for _ in range(1, K):
        sys.stdout.write(s)
else:
    for _ in range(K):
        sys.stdout.write(string)