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 main():
    n, t = map(int, input().split())
    aa, bb = input(), input()
    z = sum(a != b for a, b in zip(aa, bb))
    if t * 2 < z:
        print(-1)
        return
    res, d, ascii = [], {}, tuple("abcdefghijklmnopqrstuvwxyz")
    for a in ascii:
        for b in ascii:
            for c in ascii:
                if a != c != b:
                    d[a, b] = c
                    break
    if t >= z:
        t -= z
        for a, b in zip(aa, bb):
            if a == b:
                if t:
                    res.append(d[a, b])
                    t -= 1
                else:
                    res.append(a)
            else:
                res.append(d[a, b])
    else:
        t = t * 2 - z
        flag = True
        for a, b in zip(aa, bb):
            if a == b:
                res.append(a)
            else:
                if t:
                    res.append(d[a, b])
                    t -= 1
                else:
                    res.append(a if flag else b)
                    flag = not flag
    print(''.join(res))


if __name__ == '__main__':
    main()