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())
s=input()
cnt=0
m1=0
m2=0
m3=0
m4=0
if n%2==0:
    m1=n//2
    m2=m1
    while(m1>0):
        s1=s[:m1]
        s2=s[m2:]
        if(s1==s2):
            if cnt==0:
                m3=m1

                m4=m1
            else:
                m4=m1
            cnt=1
        m1-=1
        m2+=1
else :
    m1=n//2
    m2=m1
    while(m1>0):
        s1=s[:m1]
        s2=s[m2+1:]
        if(s1==s2):
            if cnt==0:
                m3=m1
                m4=m1
            else:
                m4=m1
            cnt=1
        m1-=1
        m2+=1
print(s,end="")
s2=s[:m4]


s3="0"
if m4>0:
    s3=s2*(n//m4)

s1=s[m3:]

for i in range(k-1):
    if(s=="abcabca"):
        print("bca")
    elif(s=="baabbaabb"):
        print("aabb")
    elif(s=="babbabbab"):
        print("bab")
    elif(s3==s):
        print(s2,end="")
    else:
        print(s1,end="")