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/python

n, t = tuple(int(i) for i in raw_input().split(" "))

s1 = list(raw_input())
s2 = list(raw_input())

def f(s1, s2):
    r = 0
    for (c1, c2) in zip(s1, s2):
        if c1 != c2: r+=1
    return r

def dc(x, y):
    c = ord('a')
    x = ord(x); y = ord(y)
    while c == x or c == y:
        c += 1
    return chr(c)


d = f(s1, s2)

if (d + 1) / 2 > t:
    print -1
    exit(0)

result = ['a'] * n

t1 = t
t2 = t

for i in xrange(n):
#    print d, t #, t1, t2
    if t < d or t1 != t2:
        if s1[i] == s2[i]:
            result[i] = s1[i]
        else:
            if t1 == t:
                result[i] = s1[i]
                t1 -= 1
            else:
                result[i] = s2[i]
                t2 -= 1
            if t1 < t and t2 < t:
                t -= 1
    elif t == d:
        if s1[i] != s2[i]:
            t -= 1
            result[i] = dc(s1[i], s2[i])
        else:
            result[i] = s1[i]
    else: # t > d
        result[i] = dc(s1[i], s2[i])
        t -= 1

    if s1[i] != s2[i]:
        d -= 1

if t:
    print -1
else:
    print "".join(result)