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:
def longestPrefixSuffix(s) :
    n = len(s)

    for res in range(n - 1, 0, -1) :

        # Check for shorter lengths
        # of first half.
        prefix = s[0: res]
        suffix = s[n - res: n]

        if (prefix == suffix) :
            return res


    # if no prefix and suffix match
    # occurs
    return 0

r = input()
n = int(r.split()[0])
k = int(r.split()[1])
# print(n, k)
s = input()
# print(s)
long_s = longestPrefixSuffix(s)
print(s,end='')
for i in range(k-1):
    print(s[long_s:],end='')
print()