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 = [int(x) for x in input().split()]
a = input()
b = input()
c = [0] * n
s = set()
otl = []
lotl = 0
for i in range(n):
    if a[i] != b[i]:
        
        otl.append(i)
        lotl += 1
    else:
        c[i] = a[i]
        s.add(i)
if lotl > (2 * t):
    print(-1)
else:
    ind1 = max(lotl - t, 0)
    ind2 = max(lotl - t, 0)
    for i in range(lotl):
        if ind1 != 0:
            c[otl[i]] = a[otl[i]]
            ind1 -= 1
        elif ind2 != 0:
            c[otl[i]] = b[otl[i]]
            ind2 -= 1
        else:
            if (chr(ord(a[otl[i]]) + 1) != b[otl[i]]) and chr(ord(a[otl[i]]) + 1) <= 'z':
                c[otl[i]] = chr(ord(a[otl[i]]) + 1)
            elif (chr(ord(a[otl[i]]) - 1) != b[otl[i]]) and chr(ord(a[otl[i]]) - 1) >= 'a':
                c[otl[i]] = chr(ord(a[otl[i]]) - 1)
            else:
                c[otl[i]] = 'l'
        t -= 1
        
    if t > 0:
        for i in s:
            if chr(ord(a[i]) + 1) <= 'z':
                c[i] = chr(ord(a[i]) + 1)
            elif chr(ord(a[i]) - 1) >= 'a':
                c[i] = chr(ord(a[i]) - 1)     
            t -=1
            if t == 0:
                break
    print(''.join(c))