CF1110H.Modest Substrings

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题目描述

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.

输入格式

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 $n$ ( $1 \le n \le 2\,000$ ).

输出格式

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.

输入输出样例

输入#1
```
1
10
3
```
输出#1
```
3
101
```
输入#2
```
1
11
3
```
输出#2
```
5
111
```
输入#3
```
12345
12346
6
```
输出#3
```
1
012345
```

说明/提示

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).

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