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
f = sys.stdin

n, t = map(int, f.readline().strip().split())

s1 = f.readline().strip()
s2 = f.readline().strip()

eq = 0
for i in range(n):
    if s1[i] == s2[i]:
        eq += 1
        
neq = n - eq
sq = []
if eq>=(n-t):
    change_n = eq-(n-t)
    for i in range(n):
        if s1[i] == s2[i]:
            #print('eq= ', i, sq, change_n)
            if change_n>0:
                if s1[i]=='a':
                    sq.append('b')
                else:
                    sq.append('a')
                change_n -= 1   
            else:
                sq.append(s1[i])
        else:
            #print('eq!= ', i, sq, change_n)
            if s1[i]=='a' or s2[i]=='a':
                if s1[i]=='b' or s2[i]=='b':
                    sq.append('c')
                else:
                    sq.append('b')
            else:
                sq.append('a')
elif (neq // ((n-t)-eq)) >= 2:
    change_n = (n-t)-eq
    step = 1
    for i in range(n):
        if s1[i] == s2[i]:
            #print('ch= ', i, sq, change_n)
            sq.append(s1[i])
        elif change_n>0 :
            #print('ch!=1 ', i, sq, change_n, step)
            if step == 1:
                sq.append(s1[i])
                step = 2
            else:
                sq.append(s2[i])
                step = 1
                change_n -= 1

        else:
            #print('ch!=2 ', i, sq, change_n, step)
            if s1[i]=='a' or s2[i]=='a':
                if s1[i]=='b' or s2[i]=='b':
                    sq.append('c')
                else:
                    sq.append('b')
            else:
                sq.append('a') 

    
else:
    sq = ['-1']    
print(''.join(sq))