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

n, t = map(int, input().split())

s1 = input()
s2 = input()
s3 = ''

def func(s1, s2, i):
    return (chr((max(ord(s1[i]) , ord(s2[i])) - 97 + 1) % 26 + 97 + (abs(ord(s1[i]) - ord(s2[i]))//25)))

mass = [0]*n
r = 0

for i in range(n):
    if s1[i] != s2[i]:
        mass[i] = 1
        r = r + 1
        
key0 = 0
cout1 = max(t - r, 0)

tmp = 2*max(r - t, 0)
tmp0 = max(r - t, 0)
key1 = 0

if t < ceil(r/2):
    print(-1)
else:
    for i in range(n):
        if s1[i] == s2[i]:
            if cout1 > 0:
                s3 = s3 + chr(((ord(s1[i]) + 1 - 97) % 26) + 97)
                cout1 = cout1 - 1
            else:
                s3 = s3 + s1[i]

        if s1[i] != s2[i]:
            if tmp > 0:
                if tmp0 > 0:
                    s3 = s3 + s1[i]
                    tmp0 = tmp0 - 1
                else:
                    s3 = s3 + s2[i]
                tmp = tmp - 1
            else:
                s3 = s3 + func(s1, s2, i)


            
print(s3)