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=map(int,(input().split()))
z=input()
ans1=""
si=0
z1=""
if n==1:
    print(k*z)
    exit(0)
for i in range(n):
    z1=z[:i+1]
    for j in range(1,n):
        z2=z[j:]
        if z2==z1:
            if len(z2)>=len(ans1):
                ans1=z2
                si=j
curr=0
for i in range(n):
    z1=z[:i+1]
    if z1==ans1:
        curr=i+1
        break
ans="";
ans+=z
ans+=z[curr:]*(k-1)
print(ans)