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:
def main():
    n, t = map(int, raw_input().split())
    s1 = raw_input().strip()
    s2 = raw_input().strip()
    same_count = 0
    for a, b in zip(s1, s2):
        if a == b:
            same_count += 1
    should_same_count = n - t
    manuel_same = should_same_count - same_count
    buf = []
    if manuel_same <= 0:
        for a, b in zip(s1, s2):
            if a != b:
                if 'a' not in (a, b):
                    buf.append('a')
                elif 'b' not in (a, b):
                    buf.append('b')
                else:
                    buf.append('c')
            else:
                if manuel_same < 0:
                    manuel_same += 1
                    if 'a' == a:
                        buf.append('b')
                    else:
                        buf.append('a')
                else:
                    buf.append(a)
        print ''.join(buf)
    elif manuel_same * 2 <= n - same_count:
        manuel_same *= 2
        for a, b in zip(s1, s2):
            if a != b:
                if manuel_same > 0:
                    if manuel_same & 1 == 1:
                        buf.append(b)
                    else:
                        buf.append(a)
                    manuel_same -= 1
                else:
                    if 'a' not in (a, b):
                        buf.append('a')
                    elif 'b' not in (a, b):
                        buf.append('b')
                    else:
                        buf.append('c')
            else:
                buf.append(a)
        print ''.join(buf)
    else:
        print -1


if __name__ == "__main__":
    main()