TriangleTriples | Topcoder Archive

Problem Statement

An ordered triple (a, b, c) is called a triangle triple if a, b, c are positive integers such that there is a triangle with side lengths a, b, c and a positive area.

For example, (4, 5, 6) and (5, 4, 6) are two different triangle triples. On the other hand, (1, 2, 3) and (47, 5, 5) are not triangle triples.

You are given the ints A, B, and C. Let X be the number of triangle triples (a, b, c) such that 1 <= a <= A, 1 <= b <= B, and 1 <= c <= C. Compute and return the value (X modulo 1,000,000,007).

Definition

Class:: TriangleTriples
Method:: count
Parameters:: int, int, int
Returns:: int
Method signature:: int count(int A, int B, int C)
(be sure your method is public)

Constraints

A will be between 1 and 1,000,000,000, inclusive.
B will be between 1 and 1,000,000,000, inclusive.
C will be between 1 and 1,000,000,000, inclusive.

Examples

```
1
```
```
10
```
```
20
```
```
Returns: 10
```
We have 10 such triples: (1,1,1), (1,2,2), (1,3,3), ..., (1,10,10).
```
2
```
```
2
```
```
1000000000
```
```
Returns: 6
```
This time we have: (1,1,1), (1,2,2), (2,1,2), (2,2,1), (2,2,2) and (2,2,3).
```
10
```
```
10
```
```
10
```
```
Returns: 505
```
```
1
```
```
1
```
```
1
```
```
Returns: 1
```

123456789

987654321

555555555

Returns: 64296241

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