SparseFactorialDiv2 | Topcoder Archive

Problem Statement

For an integer n, let F(n) = (n - 0^2) * (n - 1^2) * (n - 2^2) * (n - 3^2) * ... * (n - k^2), where k is the largest integer such that n - k^2 > 0. You are given three longs lo, hi and divisor. It is guaranteed that divisor will be a prime number. Compute and return the number of integers n between lo and hi, inclusive, such that F(n) is divisible by divisor.

Definition

Class:: SparseFactorialDiv2
Method:: getCount
Parameters:: long, long, long
Returns:: long
Method signature:: long getCount(long lo, long hi, long divisor)
(be sure your method is public)

Constraints

lo will be between 1 and 1,000,000,000,000, inclusive.
hi will be between lo and 1,000,000,000,000, inclusive.
divisor will be between 2 and 997, inclusive.
divisor will be a prime number.

Examples

```
4
```
```
8
```
```
3
```
```
Returns: 3
```
The value of F(n) for each n = 4, 5, ..., 8 is as follows. F(4) = 4*3 = 12 F(5) = 5*4*1 = 20 F(6) = 6*5*2 = 60 F(7) = 7*6*3 = 126 F(8) = 8*7*4 = 224 Thus, F(4), F(6), F(7) are divisible by 3 but F(5) and F(8) are not.
```
9
```
```
11
```
```
7
```
```
Returns: 1
```
F(9) = 9*8*5 = 360 F(10) = 10*9*6*1 = 540 F(11) = 11*10*7*2 = 1540 Only F(11) is divisible by 7.
```
1
```
```
1000000000000
```
```
2
```
```
Returns: 999999999999
```
Watch out for the overflow.
```
16
```
```
26
```
```
11
```
```
Returns: 4
```
```
10000
```
```
20000
```
```
997
```
```
Returns: 1211
```
```
123456789
```
```
987654321
```
```
71
```
```
Returns: 438184668
```

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