B. Making Sequences is Fun

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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 payS(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, coutstreams or the %I64d specifier.

Output

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

Sample test(s)

input

9 1 1

output

9

input

77 7 7

output

7

input

114 5 14

output

6

input

1 1 2

output

0

    多么典型的二分枚举呀，不过需要注意小细节。

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