Making Sequences is Fun373B

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 numbern 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 %I64dspecifier.

Output

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

Sample Input

Input

9 1 1

Output

9

Input

77 7 7

Output

7

Input

114 5 14

Output

6

Input

1 1 2

Output

0

 1 #include <stdio.h>

 2 #include <string.h>

 3 long long SS(long long a)

 4 {

 5     long long x=0;

 6     while(a>0)

 7     {

 8         a=a/10;

 9         x++;

10         //printf("%I64d\n",a);

11     }

12     return x;

13 }

14 

15 long long num(long long x)

16 {

17     long long i,y=1;

18     for(i=1;i<=x;i++)

19         y=y*10;

20     return y;

21 }

22 int main()

23 {

24     long long w,m,k;

25     int i,j;

26     while(scanf("%I64d %I64d %I64d",&w,&m,&k)!=EOF)

27     {

28         long long n=0,nu,ww,mm;

29         long long oo=SS(m);

30         nu=num(oo);

31         ww=w/k;

32         while(ww>0)

33         {

34             mm=ww/oo;

35             n=n+mm;

36             if(n>=nu-m)

37             {

38                 mm=mm-(n-nu+m);

39                 n=nu-m;

40                 ww=ww-oo*mm;

41                 oo++;

42                 nu=num(oo);

43             }

44             else

45             {

46                 ww=ww-oo*mm;

47             }

48             if(mm==0)

49                 break;

50             //printf("%I64d %I64d %I64d",ww,);

51         }

52         printf("%I64d\n",n);

53     }

54     return 0;

55 }

View Code