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())
ln = 10000000000
ans = ""
for l in range(1,n+1):
    pr = ""
    for j in range(n-l,n):
        pr+=t[j]
    pr = t+pr*(k-1)
    count = 0
    #print(pr)
    for start in range(0,len(pr)-n+1):
        f = True
        for kl in range(start,start+n):
            #print(pr[k])
            #print(t[k-start])
            if(pr[kl]!=t[kl-start]):
                f = False
                break
        if(f):
            count += 1
    #print(count)
    if(count==k):
        #print(count)
        #print(k)
        if(len(pr)<=ln):
            ln = len(pr)
            ans = pr
print(ans)