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,kk = map(int,(input().split()))
zz = input()
z = [0 for i in range(n)]
l=0
r=0
for i in range(1,len(z)):
    if i > r:
        r=l=i
        while r < len(z) and zz[r] == zz[r-l]:
            r += 1
        z[i] = r-l
        r -= 1
    else:
        k = i-l
        if  z[k] < r-i+1:
            z[i] = z[k]
        else:
            l = i
            while r < len(z) and zz[r] == zz[r-l]:
                r += 1
            z[i] = r-l
            r -= 1
c = 0
f = 0
for i in range(len(z)-1,-1,-1):
    if z[i]>0:
        if len(z)-i==z[i]:
            c = max(c,z[i])
            f = 1

#print(c)
print(zz+(kk-1)*zz[c:])