Look at the following sequence:3, 5, 6, 9, 10, 12, 17, 18, 20....All the numbers in the series have exactly 2 bits set in their binary representation. Your task is simple, you have to find the Nth number of this sequence.Input FormatThe first line of input contains T - the number of test cases. It's followed by T lines, each containing a single number N.Output FormatFor each test case, print the Nth number of the sequence, separated by a newline. Since the number can be very large, print the number % 1000000007.Constraints30 points1 <= T, N <= 20070 points1 <= T, N <= 105100 points1 <= T <= 1051 <= N <= 1014ExampleInput512550100Output3510104016640
Question
Look at the following sequence:3, 5, 6, 9, 10, 12, 17, 18, 20....All the numbers in the series have exactly 2 bits set in their binary representation. Your task is simple, you have to find the Nth number of this sequence.Input FormatThe first line of input contains T - the number of test cases. It's followed by T lines, each containing a single number N.Output FormatFor each test case, print the Nth number of the sequence, separated by a newline. Since the number can be very large, print the number % 1000000007.Constraints30 points1 <= T, N <= 20070 points1 <= T, N <= 105100 points1 <= T <= 1051 <= N <= 1014ExampleInput512550100Output3510104016640
Solution
This problem is about finding the Nth number in a sequence where all numbers have exactly 2 bits set in their binary representation.
Here are the steps to solve this problem:
- Initialize a variable to store the result.
- Create a loop from 1 to N.
- In each iteration, calculate the binary representation of the current number.
- Check if the binary representation has exactly 2 bits set. If it does, increment the result.
- Continue this process until you reach the Nth number that satisfies the condition.
- After the loop, print the result modulo 1000000007.
This is a brute force solution and may not be efficient for large inputs. For larger inputs, you may need to use a more optimized approach, such as using dynamic programming or bitwise operations to calculate the number of set bits more efficiently.
Please note that this is a high-level solution. The actual implementation will depend on the programming language you are using.
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