Making Sequences is Fun

2000ms

262144K

Description:

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.

Input:

The first line contains three integers w (1 ≤ w ≤ 10¹⁶), m (1 ≤ m ≤ 10¹⁶), k (1 ≤ k ≤ 10⁹).

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.

Output:

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

Sample Input:

9 1 1

Sample Output:

Sample Input:

77 7 7

Sample Output:

Sample Input:

114 5 14

Sample Output:

Sample Input:

1 1 2

Sample Output:

Informação

Provedor Codeforces

Código CF373B