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:
import math
n,k=map(int,input().split())
t=input()
c=0
temp=0
for i in range(1,n):
    for j in range(0,n-i):
        if(t[j]==t[j+i]):
            c=c+1
        else:
            break
    if(c==n-i and c>temp):
        temp=c
    c=0
        #else:
            #if(c>temp):
                #temp=c
            #c=0
            #break






"""for i in range(0,math.ceil(n/2)):
    if(t[i]==t[n-i-1]):
        c=c+1
    else:
        break
print(c)"""
ans=t
for i in range(0,k-1):
    ans=ans+t[temp:]
#ans=n+(n-c)*(k-1)
print(ans)