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 PYTHON):

Solution:
from sys import stdin

rstr = lambda: stdin.readline().strip()
rints = lambda: [int(x) for x in stdin.readline().split()]


def kmp_table(pat):
    l, fail, k = len(pat), [0] * (len(pat)), 0

    for i in range(1, l):
        while (k and pat[k] != pat[i]):
            k = fail[k - 1]

        if pat[k] == pat[i]:
            fail[i] = k + 1
            k += 1
        else:
            fail[i] = k
    return fail


n, k = rints()
s = rstr()
print(s + s[kmp_table(s)[-1]:] * (k - 1))