FairSplit | Topcoder Archive

Problem Statement

Vegard and Bard have some packs of sweets: for each i between A and B, inclusive, they have one pack that contains i sweets. The pair (A, B) is called fair if Vegard and Bard can divide the packs among themselves in such a way that each of them gets the same total number of sweets.

Count all fair pairs (A, B) such that A <= B, loA <= A <= hiA, and loB <= B <= hiB.

Definition

Class:: FairSplit
Method:: count
Parameters:: int, int, int, int
Returns:: long
Method signature:: long count(int loA, int hiA, int loB, int hiB)
(be sure your method is public)

Constraints

1 <= loA <= hiA <= 2,000,000,000.
1 <= loB <= hiB <= 2,000,000,000.

Examples

```
7
```
```
7
```
```
1
```
```
15
```
```
Returns: 3
```
A must be 7, and B must be between 1 and 15, inclusive. There are three fair pairs that match these constraints: (7,10), (7,13), and (7,14). In the first case, Vegard can take 7+10 sweets. In the second case, Vegard can take 10+12+13 sweets. In the third case, Vegard can take 7+10+12+13 sweets. We can easily verify that in each of those cases Bard will get the same number of sweets as Vegard.
```
101
```
```
200
```
```
1
```
```
100
```
```
Returns: 0
```
For these constraints we cannot have A <= B, so there is no fair pair that matches these constraints.
```
1
```
```
4
```
```
5
```
```
10
```
```
Returns: 11
```
```
4
```
```
17
```
```
12
```
```
33
```
```
Returns: 129
```

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