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:
from math import ceil, floor


def round1(x):
    return ceil(x) if (x - int(x) >= .5) else floor(x)


def get_char(x, y):
    for i in range(ord('a'), ord('z') + 1):
        if chr(i) not in [x, y]:
            return chr(i)


n, t = map(int, input().split())
s1, s2, mi = input(), input(), 0

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

mi1 = mi / 2

if t < round1(mi1):
    print(-1)
else:
    ans, ext, c = ['' for i in range(n)], max(t - mi, 0), 0
    mi = min(t, mi)

    for i in range(n):
        if s1[i] != s2[i]:
            if mi != mi1:
                mi -= 1
                mi1 -= .5
                ans[i] = get_char(s1[i], s2[i])
            else:
                mi -= 1
                mi1 -= 1
                ans[i] = s1[i] if c % 2 else s2[i]
                c += 1
        else:
            if ext:
                ans[i] = get_char(s1[i], s2[i])
                ext -= 1
            else:
                ans[i] = s1[i]

    print(''.join(ans))