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:
n, t = map(int, raw_input().strip().split(' '))
s1 = raw_input().strip()
s2 = raw_input().strip()
if t > n:
    print -1
    exit(0)
d = 0
for i in xrange(len(s1)):
    if s1[i] != s2[i]:
        d += 1
left = t
stokill = 0
dtokill = 0
dtokillhalf = 0
if d % 2 == 1:
    left -= 1
    d -= 1
    dtokill += 1
if d / 2 > left:
    print -1
    exit(0)
if left >= d:
    stokill += left - d
    dtokill += d
elif d > 2 * left:
    print -1
    exit(0)
else:
    dtokillhalf += (d - left) * 2
    dtokill += d - (d - left) * 2
result = []


def diff(a, b):
    return 'a' if 'a' not in [a, b] else 'b' if 'b' not in [a, b] else 'c'


for i in xrange(len(s1)):
    if s1[i] != s2[i]:
        if dtokill:
            result.append(diff(s1[i], s2[i]))
            dtokill -= 1
        elif dtokillhalf:
            result.append(s1[i] if dtokillhalf % 2 == 0 else s2[i])
            dtokillhalf -= 1
    else:
        if stokill:
            result.append(diff(s1[i], s2[i]))
            stokill -= 1
        else:
            result.append(s1[i])
print ''.join(result)