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:
#!/usr/bin/env python
from sys import stdin as cin

P = 10**9+7

def other_than(c1, c2):
    if c1 != 'a' and c2 != 'a':
        return 'a'
    if c1 != 'b' and c2 != 'b':
        return 'b'
    return 'c'

def main():
    n, t = map(int, next(cin).split())
    s1 = next(cin).strip()
    s2 = next(cin).strip()
    difn = sum(c1 != c2 for (c1,c2) in zip(s1, s2))

    change_neqs = 0
    if difn % 2:
        change_neqs += 1
        difn -= 1
        n -= 1
        t -= 1

    if t < difn // 2:
        return '-1'

    change_eqs = 0
    if t > difn:
        change_eqs = t - difn
        t = difn

    change_neq1 = change_neq2 = difn - t
    change_neqs += difn - change_neq1*2

    s = []
    for (c1, c2) in zip(s1, s2):
        if c1 == c2:
            if change_eqs:
                c = other_than(c1, c2)
                change_eqs -= 1
            else:
                c = c1
        else:
            if change_neqs:
                c = other_than(c1, c2)
                change_neqs -= 1
            elif change_neq1:
                c = c2
                change_neq1 -= 1
            elif change_neq2:
                c = c1
                change_neq2 -= 1
            else:
                raise Exception('bad condition')
        s.append(c)

    return ''.join(s)


print main()