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:
def solve(s,n):
  s="".join(s)
  n+=1
  count=n-1
  for i in range(n-1):
    if s[:count] == s[n-count:n]:
      break
    count-=1 
  return count

def make_table(pattern,unique):
  table=[]
  k=0
  current=[]
  for i in range(len(pattern)+1):
    current.append("")
  for i in pattern:
    table.append([])
    for j in unique:
      if i is not j:
        current[k]=j
        table[k].append(solve(current,k))
      else:
        table[k].append(k+1)
    current[k]=pattern[k]
    k+=1  
  table.append([])
  for j in unique:
    current[k]=j
    table[k].append(solve(current,k))  
  return table  

def find(text,table,d):
  count=0
  current=0
  k=0
  for i in text:
    if i in d.keys():
      current=table[current][d[i]]
    else:
      current=0
    if current==len(table)-1:
      #print(k-len(table)+2)
      count+=1 
    k+=1
  return count

#print("Enter Text")
#text=input().strip()
#print("Enter pattern")
#pattern=input().strip()
n,k=map(int,input().split())
pattern=input().strip()
unique=set()
for i in pattern:
  unique.add(i)
unique=list(unique)
unique.sort()
table=make_table(pattern,unique)
d={}
t=max(table[len(table)-1])-1
ans=pattern[:]
k-=1
for i in range(k):
    ans+=pattern[t:]
print(ans)