Largest number less than equal to N having exactly K set bits

Given two positive integers N and K, we need to determine if there exists a positive integer X less than or equal to N such that the number of 1s in the binary representation of X is equal to k (i.e., f(X) = K). If such an X exists, we also need to find the maximum value of X and print -1 if there is no such positive integer X.

Constraints:

1 <= X <=10⁹
0 <= K <= 31

Examples:

Input: X = 8, K = 2
Output:6

Input: X = 9, K = 4
Output: -1

Approach: Follow the steps to solve the problem:

• Count the number of set bits in the integer X.
• If a number of set bits is equal to K then return that number itself.
• Else traverse every bit of the number.
• If the number of set bits in X is less than the required set bits (K).
• Then count the number of non set bits we have to convert from the current bit and toggle them.
• Else count the number of set bits we have to convert from 1's to 0's and toggle them from right to left.
• If no such number is possible to create return -1.
• Else return that maximum number which is less than X and has total K set bits.

Below is the implementation for the above approach:

6
-1

Time Complexity: O(Log(N))
Auxiliary Space: O(1)