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=input().split()
n,k=int(n),int(k)
t=input()
j=0
p=1
z=1
i=1
while(i<n):
    if(t[j]==t[i]):
        j+=1
        z=1
    else:
        j=0
        z=1
        if(p!=1):
            i=p
            p=1
            z=0
    if(t[0]==t[i] and j==0 and z!=0):
        j=1
    if(t[0]==t[i] and j>1 and i!=n-1):
        p=i
    if(z!=0):
        i+=1
if(j==0):
    s=''
    for i in range(k):
        s=s+t
    print(s)
else:
    s=''
    s=s+t
    t=t[j:n]
    for i in range(1,k):
        s=s+t
    print(s)