H. Modest Substrings
time limit per test
5 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

You are given two integers $l$ and $r$.

Let's call an integer $x$ modest, if $l \le x \le r$.

Find a string of length $n$, consisting of digits, which has the largest possible number of substrings, which make a modest integer. Substring having leading zeros are not counted. If there are many answers, find lexicographically smallest one.

If some number occurs multiple times as a substring, then in the counting of the number of modest substrings it is counted multiple times as well.

Input

The first line contains one integer $l$ ($1 \le l \le 10^{800}$).

The second line contains one integer $r$ ($l \le r \le 10^{800}$).

The third line contains one integer $n$ ($1 \le n \le 2\,000$).

Output

In the first line, print the maximum possible number of modest substrings.

In the second line, print a string of length $n$ having exactly that number of modest substrings.

If there are multiple such strings, print the lexicographically smallest of them.

Examples
Input
1
10
3

Output
3
101

Input
1
11
3

Output
5
111

Input
12345
12346
6

Output
1
012345

Note

In the first example, string «101» has modest substrings «1», «10», «1».

In the second example, string «111» has modest substrings «1» ($3$ times) and «11» ($2$ times).