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

def s(c1, c2):
    if c2 < c1:
        c1, c2 = c2, c1
    if c1 == 'a':
        if c2 == 'b':
            return 'c'
        else:
            return 'b'
    else:
        return 'a'

n, t = [int(x) for x in input().split()]
s1, s2 = input(), input()

cdiff, csame = [], []
for i, c1, c2 in zip(range(n), s1, s2):
    if c1 == c2:
        csame.append(i)
    else:
        cdiff.append(i)

out = [''] * n
d = n - t - len(csame)

if n - t <= len(csame):
    for i in csame[:n-t]:
        out[i] = s1[i]
    for i in range(n):
        if out[i] == '':
            out[i] = s(s1[i], s2[i])
    print(''.join(out))

elif len(cdiff) >= 2 * d:
    for i in csame[:n-t]:
        out[i] = s1[i]
    for i in cdiff[:d]:
        out[i] = s1[i]
    for i in cdiff[d:2*d]:
        out[i] = s2[i]
    for i in cdiff[2*d:]:
        out[i] = s(s1[i], s2[i])
    print(''.join(out))

else:
    print(-1)