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:
n, t = map(int, input().split())
s1 = str(input())
s2 = str(input())
s3 = list()
for i in range(n):
    s3.append(ord('a'))
c1, c2 = 0, 0
su = 0
for i in range(n):
    su += (s1[i] != s2[i])
changed = [0 for i in range(n)]
for i in range(n):
    if s1[i] != s2[i]:
        if (su != 1 or (su == 1 and abs(c2-c1) == 1)):
            if c1 <= c2:
                c1 += 1
                s3[i] = ord(s1[i])
                changed[i] = 1
            else:
                c2 += 1
                s3[i] = ord(s2[i])
                changed[i] = 2
        else:
            if s1[i] != 'a' and s2[i] != 'a':
                s3[i] = ord('a')
            elif s1[i] != 'b' and s2[i] != 'b':
                s3[i] = ord('b')
            else:
                s3[i] = ord('c')
            c1 += 1
            c2 += 1
            changed[i] = 3
        su -= 1
    else:
        s3[i] = ord(s1[i])
for i in range(n):
    if t - c1 > 0 and changed[i] == 0:
        if s1[i] != 'a' and s2[i] != 'a':
            s3[i] = ord('a')
        elif s1[i] != 'b' and s2[i] != 'b':
            s3[i] = ord('b')
        else:
            s3[i] = ord('c')
        c1 += 1
        c2 += 1
for i in range(n):
    if t - min(c1, c2) > 0 and (changed[i] == 1 or changed[i] == 2):
        if s1[i] != 'a' and s2[i] != 'a':
            s3[i] = ord('a')
        elif s1[i] != 'b' and s2[i] != 'b':
            s3[i] = ord('b')
        else:
            s3[i] = ord('c')
        if changed[i] == 1:
            c2 += 1
        else:
            c1 += 1
if t != c1:
    print(-1)
else:
    for i in range(n):
        print(chr(s3[i]), end='')