In this problem we consider unsigned 30-bit integers, i.e. all integers B such that 0 ≤ B < 2³⁰.

We say that integer A conforms to integer B if, in all positions where B has bits set to 1, A has corresponding bits set to 1.

For example:

• 00 0000 1111 0111 1101 1110 0000 1111(BIN) = 16,244,239 conforms to
  00 0000 1100 0110 1101 1110 0000 0001(BIN) = 13,032,961, but
• 11 0000 1101 0111 0000 1010 0000 0101(BIN) = 819,399,173 does not conform to
  00 0000 1001 0110 0011 0011 0000 1111(BIN) = 9,843,471.

Write a function:

Private Function solution(A As Integer, B As Integer, C As Integer) As Integer

that, given three unsigned 30-bit integers A, B and C, returns the number of unsigned 30-bit integers conforming to at least one of the given integers.

For example, for integers:

• A = 11 1111 1111 1111 1111 1111 1001 1111(BIN) = 1,073,741,727,
• B = 11 1111 1111 1111 1111 1111 0011 1111(BIN) = 1,073,741,631, and
• C = 11 1111 1111 1111 1111 1111 0110 1111(BIN) = 1,073,741,679,

the function should return 8, since there are 8 unsigned 30-bit integers conforming to A, B or C, namely:

• 11 1111 1111 1111 1111 1111 0011 1111(BIN) = 1,073,741,631,
• 11 1111 1111 1111 1111 1111 0110 1111(BIN) = 1,073,741,679,
• 11 1111 1111 1111 1111 1111 0111 1111(BIN) = 1,073,741,695,
• 11 1111 1111 1111 1111 1111 1001 1111(BIN) = 1,073,741,727,
• 11 1111 1111 1111 1111 1111 1011 1111(BIN) = 1,073,741,759,
• 11 1111 1111 1111 1111 1111 1101 1111(BIN) = 1,073,741,791,
• 11 1111 1111 1111 1111 1111 1110 1111(BIN) = 1,073,741,807,
• 11 1111 1111 1111 1111 1111 1111 1111(BIN) = 1,073,741,823.

Write an efficient algorithm for the following assumptions:

• A, B and C are integers within the range [0..1,073,741,823].