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

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

s1 = input()
s2 = input()

same = sum([1 for i in range(n) if s1[i] ==s2[i]])

def other(c1, c2):
    ans = 'a'
    while ans == c1 or ans == c2:
        ans = chr(ord(ans) + 1)
    return ans

if same + 2 * t < n:
    print(-1)
    sys.exit(0)

samehave = 0
sames1 = 0
sames2 = 0

ans = ['v'] * n

for i in range(n):
    if s1[i] == s2[i]:
        if sames1 < n - t and sames2 < n - t:
            ans[i] = s1[i]
            sames1 += 1
            sames2 += 1
        else:
            ans[i] = other(s1[i], s2[i])

for i in range(n):
    if s1[i] != s2[i]:
        if sames1 < n - t:
            sames1 += 1
            ans[i] = s1[i]
        elif sames2 < n - t:
            sames2 += 1
            ans[i] = s2[i]
        else:
            ans[i] = other(s1[i], s2[i])
        

print(*ans, sep='')