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 PYTHON):

Solution:
def func(c1,c2):
    if c1!="a" and c2!="a":
        return "a"
    elif c1=="a" and c2!="b":
        return "b"
    elif c2=="a" and c1!="b":
        return "b"
    else:
        return "c"

n,t = map(int,raw_input().split())
s1 = raw_input()
s2 = raw_input()

ns = 0
nd = 0
cmpr = [0]*n
for i in range(n):
    if s1[i]==s2[i]:
        cmpr[i] = 1
        ns += 1
nd = n - ns

if t < (nd+1)/2:
    print -1
else:
    ans = [0]*n
    s = n - t
    s1s = 0
    s2s = 0
    if ns>=s:
        cnt = 0
        for i in range(n):
            if cmpr[i] == 1 and cnt < s:
                ans[i] = s1[i]
                cnt += 1
            else:
                ans[i] = func(s1[i],s2[i])
    else:
        for i in range(n):
            if cmpr[i] == 1:
                ans[i] = s1[i]
                s1s += 1
                s2s += 1
        for i in range(n):
            if cmpr[i]!=1:
                if s1s<s:
                    ans[i] = s1[i]
                    s1s += 1
                elif s2s<s:
                    ans[i] = s2[i]
                    s2s += 1
                else:
                    ans[i] = func(s1[i],s2[i])
    print "".join(i for i in ans)