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:
def generate(first_char,second_char):
    if (first_char != 'a' and second_char != 'a'):
        return 'a'
    elif (first_char != 'b' and second_char != 'b'):
        return 'b'
    else:
        return 'c'

def right_answer(first,second,length):
    res=0
    for i in range(length):
        if first[i]!=second[i]:
            res+=1
    return res

n,t = [int(i) for i in input().split()]
first,second,third,equal,dif = list(input()),list(input()),["a"]*n,[False]*n,0
for i in range(n):
    if first[i]!=second[i]:
        dif+=1
    else:
        equal[i]=True
if t==dif:
    for i in range(n):
        third[i] = first[i] if (equal[i]) else generate(first[i],second[i])
elif t>dif:
    counter = 0
    for i in range(n):
        if equal[i]:
            if counter<(t-dif):
                third[i]=generate(first[i],second[i])
                counter+=1
            else:
                third[i]=first[i]
        else:
            third[i]=generate(first[i],second[i])
else:
    counter1,counter2=0,0
    for i in range(n):
        if equal[i]:
            third[i]=first[i]
        else:
            if counter1<(dif-t):
                third[i]=first[i]
                counter1+=1
            elif counter2<(dif-t):
                third[i]=second[i]
                counter2+=1
            else:
                third[i]=generate(first[i],second[i])
if right_answer(first,third,n)==t and right_answer(second,third,n)==t:
    print(''.join(third))
else:
    print("-1")