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())
t = str(input())

def z_algorithm(s):
    n = len(s)
    Z = [0]*n
    Z[0] = n
    i = 1
    j = 0
    while i < n:
        while i+j < n and s[j] == s[i+j]:
            j += 1
        Z[i] = j
        if j == 0:
            i += 1
            continue
        k = 1
        while i+k < n and k+Z[k] < j:
            Z[i+k] = Z[k]
            k += 1
        i += k
        j -= k
    return Z

z = z_algorithm(t)
#print(z)
if n == 1:
    print(t*k)
    exit()
for i in range(1, n):
    if z[i] == n-i:
        print(t[0:i]*k+t[i:])
        exit()
else:
    print(t*k)