PyramidSequences | Topcoder Archive

Problem Statement

A pyramid sequence of height X > 1 is an infinite sequence of positive integers with period 2X-2. Its first 2X-2 terms are 1, 2, ..., X-1, X, X-1, ..., 2.

You are given ints N and M. Consider two pyramid sequences A and B, A of height N and B of height M. Return the number of distinct pairs of integers (x,y) such that for some i > 0 we have x=A[i] and y=B[i].

Definition

Class:: PyramidSequences
Method:: distinctPairs
Parameters:: int, int
Returns:: long
Method signature:: long distinctPairs(int N, int M)
(be sure your method is public)

Constraints

N will be between 2 and 1,000,000,000, inclusive.
M will be between 2 and 1,000,000,000, inclusive.

Examples

```
3
```
```
4
```
```
Returns: 6
```
These are the first several terms of pyramid sequences of height 3 and 4: {1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1} {1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1} We can see the following pairs: (1, 1), (2, 2), (3, 3), (2, 4), (1, 3), (3, 1). No other pairs will appear later in the sequences.
```
3
```
```
5
```
```
Returns: 5
```
The sequences begin with: {1, 2, 3, 2, 1, 2, 3, 2, 1} {1, 2, 3, 4, 5, 4, 3, 2, 1}
```
43
```
```
76
```
```
Returns: 895
```
```
2
```
```
1000000000
```
```
Returns: 1000000000
```
```
100000
```
```
95555
```
```
Returns: 4777750000
```

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