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 PYTHON):

Solution:
__author__ = 'aste'


def main():
    n, t = map(int, raw_input().split())
    s1 = raw_input()
    s2 = raw_input()

    diff = 0
    for i in range(0, n):
        if s1[i] != s2[i]:
            diff += 1

    match_needed = n - t
    diff_cap = diff / 2
    eq_cap = n - diff
    if diff_cap + eq_cap < match_needed:
        print -1
    else:
        res = ['0'] * n
        matched = 0
        double_diff_cap = 2 * diff_cap
        double_match_needed = 2 * match_needed

        # match from equal set
        for i in range(0, n):
            if matched == double_match_needed:
                break
            if s1[i] == s2[i]:
                if eq_cap > 0:
                    res[i] = s1[i]
                    eq_cap -= 1
                    matched += 2

        # match from non-equal set
        for i in range(0, n):
            if matched == double_match_needed:
                break
            if s1[i] != s2[i]:
                if double_diff_cap > 0:
                    if double_diff_cap % 2 == 0:
                        res[i] = s1[i]
                    else:
                        res[i] = s2[i]
                    double_diff_cap -= 1
                    matched += 1

        # do not match is what's left
        alphabet = set('abcdefghijklmnopqrstuvwxyz')
        for i in range(0, n):
            if res[i] == '0':
                res[i] = list(alphabet.difference(set([s1[i], s2[i]])))[0]
        print "".join(res)

if __name__ == "__main__":
    main()