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:
n, t = map(int, input().split())
str1 = list(input())
str2 = list(input())

def choice(a, b):
    for i in range(3):
        c = chr(i + ord('a'))
        if c != a and c != b:
            return c

common = [i for i in range(n) if str1[i] == str2[i]]
lc = len(common) # num of equal chars
ld = n - lc # num of different chars

if ld // 2 + lc < n - t:
    print(-1)
    exit()

dist = n
changes_diff = 2 * min(n - t, (ld // 2))
dist -= changes_diff // 2

ans = [-1] * n
flag = True
for k, (a, b) in enumerate(zip(str1, str2)):
    if changes_diff > 0:
        if a != b:
            ans[k] = a if flag else b
            flag = not flag
            changes_diff -= 1
    else:
        ans[k] = choice(a, b)

changes_comm = t - changes_diff // 2

for k, (a, b) in enumerate(zip(str1, str2)):
    if dist - t > 0:
        if a == b:
            ans[k] = a
            dist -= 1
    else:
        if a == b:
            ans[k] = choice(a, b)


print(''.join(ans))