Problem: Marina loves strings of the same length and Vasya loves when there is a third string, different from them in exactly t characters. Help Vasya find at least one such string.

More formally, you are given two strings s1, s2 of length n and number t. Let's denote as f(a, b) the number of characters in which strings a and b are different. Then your task will be to find any string s3 of length n, such that f(s1, s3) = f(s2, s3) = t. If there is no such string, print  - 1.

Input

The first line contains two integers n and t (1 ≤ n ≤ 105, 0 ≤ t ≤ n).

The second line contains string s1 of length n, consisting of lowercase English letters.

The third line contain string s2 of length n, consisting of lowercase English letters.

Output

Print a string of length n, differing from string s1 and from s2 in exactly t characters. Your string should consist only from lowercase English letters. If such string doesn't exist, print -1.

Examples

Input

3 2
abc
xyc


Output

ayd

Input

1 0
c
b


Output

-1

Solution (in PYTHON3):

Solution:

def other(ch1, ch2):
    for char in 'abc':
        if (ch1 != char) and (ch2 != char):
            return char


n, t = list(map(int, input().split()))

s1 = input()
s2 = input()

diff = 0
for ch1, ch2 in zip(s1, s2):
    if ch1 != ch2:
        diff += 1
same = n - diff

if (n < t) or (2 * t < diff):
    print(-1)
else:
    changediff = min(t, diff)
    changesame = max(0, t - diff)
    res = [None] * n
    samefirst, samesecond = (diff-t), (diff-t)
    i = -1 
    for ch1, ch2 in zip(s1, s2):
        i += 1
        if ch1 == ch2:
            if changesame:
                #res += other(ch1, ch2)
                res[i] = other(ch1, ch2)
                changesame -= 1
            else:
                #res += ch1
                res[i] = ch1
        else:
            if changediff == diff:
                #res += other(ch1, ch2)
                res[i] = other(ch1, ch2)
            else:
                if samefirst:
                    #res += ch1
                    res[i] = ch1
                    samefirst -= 1
                elif samesecond:
                    #res += ch2
                    res[i] = ch2
                    samesecond -= 1
                else:
                    #res += other(ch1, ch2)
                    res[i] = other(ch1, ch2)
    print("".join(map(str, res)))