YetAnotherORProblem | Topcoder Archive

Problem Statement

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You're given a long[] R containing N elements. Count the number of sequences A₀, A₁, ..., A_N-1 such that each A_i is an integer satisfying 0 &le A_i &le R[i] and A₀ + A₁ + ... + A_N-1 = A₀ | A₁ | ... | A_N-1. The '|' symbol stands for bitwise OR of the operands. Return the number of such sequences modulo 1,000,000,009.

Definition

Class:: YetAnotherORProblem
Method:: countSequences
Parameters:: long[]
Returns:: int
Method signature:: int countSequences(long[] R)
(be sure your method is public)

Notes

If a and b are single bits then a | b is defined as max(a, b). For two integers, A and B, in order to calculate A | B, they need to be represented in binary: A = (an...a1)2, B = (bn...b1)2 (if the lengths of their representations are different, the shorter one is prepended with the necessary number of leading zeroes). Then A | B = C = (cn...c1)2, where ci = ai | bi. For example, 10 | 3 = (1010)2 | (0011)2 = (1011)2 = 11.

Constraints

R will contain between 2 and 10 elements, inclusive.
Each element of R will be between 1 and 10^18, inclusive.

Examples

```
{3,5}
```
```
Returns: 15
```
All the possible sequences are: {0,0}, {0,1}, {0,2}, {0,3}, {0,4}, {0,5}, {1,0}, {1,2}, {1,4}, {2,0}, {2,1}, {2,4}, {2,5}, {3,0}, {3,4}.
```
{3,3,3}
```
```
Returns: 16
```
```
{1,128}
```
```
Returns: 194
```
```
{26,74,25,30}
```
```
Returns: 8409
```

{1000000000,1000000000}

Returns: 420352509

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