A9361 | Making Sequences is Fun

We'll define $S(n)$ for positive integer $n$ as follows: the number of the $n$ 's digits in the decimal base. For example, $S(893)=3$ , $S(114514)=6$ .

You want to make a consecutive integer sequence starting from number $m$ ( $m,m+1,...$ ). But you need to pay $S(n)·k$ to add the number $n$ to the sequence.

You can spend a cost up to $w$ , and you want to make the sequence as long as possible. Write a program that tells sequence's maximum length.

The first line contains three integers $w$ ( $1<=w<=10^{16}$ ), $m$ ( $1<=m<=10^{16}$ ), $k$ ( $1<=k<=10^{9}$ ).

Please, do not write the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

The first line should contain a single integer — the answer to the problem.