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:
# cook your code here
l = raw_input().strip().split()
n, k = int(l[0]), int(l[1])

t = raw_input()



def computeLPSArray(pat):
    lps = [0]*len(pat)
    j = 0 
    lps[0] = 0
    i = 1
    while i < len(pat):
        if pat[i]==pat[j]:
            j += 1
            lps[i] = j
            i += 1
        else:
            if j != 0:
                j = lps[j-1]
            else:
                lps[i] = 0
                i += 1
    return lps[len(pat)-1]

x = len(t) - computeLPSArray(t)
tn = t[:x]
last = t[x:]

ans = ""
while k>0:
    ans += tn
    k-=1

print ans+last