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:
#!/usr/bin/python3
# -*- coding: <utf-8> -*-

import itertools as ittls
from collections import Counter
from functools import reduce

import string
import math


def sqr(x):
    return x*x

def inputarray(func = int):
    return map(func, input().split())

# -------------------------------
# -------------------------------

n, t = inputarray()
s1 = input()
s2 = input()

d = sum(map(lambda x,y: x!=y, s1, s2))

if t < (d + 1)//2:
    print(-1)
    quit()


def nt(x, y):
    s = set(['a','b','c']) - set([x, y])
    return s.pop()

if t >= d:
    res, v = '', 0
    for i, j in zip(s1, s2):
        if i != j:
            res = res + nt(i,j)
        else:
            if v < t - d:
                res = res + nt(i, j)
                v = v + 1
            else:
                res = res + i

    print(res)
else:
    res, k = '', 0
    for i, j in zip(s1, s2):
        if i == j:
            res = res + i
        else:
            if d == t:
                res = res + nt(i, j)
                t = t - 1
            else:
                if k == 0:
                    res = res + i
                    t = t - 1
                else:
                    res = res + j

                k = 1 - k

            d = d - 1

    if d != 0 or t != 0:
        print(-1)
    else:
        print(res)