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:
data = input().split()
k = int(data[1]) 
s_0 = list(input()) 
s = list() 
h = 1
fl2 = True 
for i in s_0:
    s.append(i) 
k_was = 1 
if (len(s_0) == 1):
   for t in range(1,k):
       s.append(s_0[0])
   k_was = k+10
while(k_was < k): 
    j = 0
    x = 0
    while (not ((h > len(s)-1) or (j > len(s_0)-1))): 
        if (s[h] == s_0[j]): 
            if (fl2): x = h; fl2 = False
            j+=1 
            fl1=True 
            h+=1 
        else: 
            if not fl2: h = x + 1
            else: h += 1
            fl2 = True
            fl1 = False
            j = 0
  
    if (fl1): 
            for p in range(x,x+len(s_0)): 
                if (p >= len(s)):
                    s.append(s_0[p-x])
                else:
                    s[p]=s_0[p - x]
                
            h = x + 1
            j = 0
            k_was+=1
            fl2 = True

            
    else:
             for p in s_0: 
                 s.append(p)
             k_was+=1
             h = h + 1
             j = 0
             fl2 = True
f = ''
for t in range(0,len(s)):
    f += s[0]
    del(s[0])
    
print(f)