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:
#import sys
#sys.stdin = open("python/in", "r")

n, k = [int(i) for i in input().split(" ")]
s = input()
t = input()
same = 0
for i in range(n):
    if s[i] == t[i]:
        same += 1

diff = n - same
min_diff = n - (same + (diff // 2) )
if min_diff > k:
    print (-1)
else:
    #construct
    ans = {}
    simm = 0
    req = n - k
    i = 0
    f = True
    while simm < req:
        if s[i] == t[i]:
            ans[i] = s[i]
            simm += 1
        elif f:
            aha = i
            f = not f
        else:
            ans[aha] = s[aha]
            ans[i] = t[i]
            f = not f
            simm += 1
        i += 1
    if f == False:
        if ('a' != s[aha]) and ('a' != t[aha]):
            ans[aha] = 'a'
        elif ('b' != s[aha]) and ('b' != t[aha]):
            ans[aha] = 'b'
        elif ('c' != s[aha]) and ('c' != t[aha]):
            ans[aha] = 'c'
        else:
            ans[aha] = 'd'
    
    #make rest diferent
    while i < n:
        if ('a' != s[i]) and ('a' != t[i]):
            ans[i] = 'a'
        elif ('b' != s[i]) and ('b' != t[i]):
            ans[i] = 'b'
        elif ('c' != s[i]) and ('c' != t[i]):
            ans[i] = 'c'
        else:
            ans[i] = 'd'
        i += 1
    for i in range(n):
        print(ans[i], end='')
    print()