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:
def computeLPSArray(pat, M):
    j = 0 # jgth of the previous longest prefix suffix
    lps = [0]*M
    lps[0] # lps[0] is always 0
    i = 1
 
    # the loop calculates lps[i] for i = 1 to M-1
    while i < M:
        if pat[i]== pat[j]:
            j += 1
            lps[i] = j
            i += 1
        else:
            # This is tricky. Consider the example.
            # AAACAAAA and i = 7. The idea is similar 
            # to search step.
            if j != 0:
                j = lps[j-1]
 
                # Also, note that we do not increment i here
            else:
                lps[i] = 0
                i += 1
    return lps[M-1]


n,k = map(int,raw_input().strip('\n').split(' '))
t = raw_input()
l = computeLPSArray(t,n)
repeating = t[l:]
s = t+repeating*(k-1)
print s