# Find Kth smallest value for b such that a + b = a | b

Given a number a and k, the task is to find the k’th smallest value for b such that a + b = a | b, where ‘|’ denotes the bitwise OR operator. The maximum value of a and k can be .

Examples:

```Input: a = 10, k = 3
Output: 5
Numbers satisfying the condition 5 + b = 5 | b
are 1, 4, 5, etc.
Since 3rd smallest value for b is required,
hence b = 5.

Input: a = 1, k = 1
Output: 2
Numbers satisfying the condition 1 + b = 1 | b
are 2, 4, 6, etc.
Since 1st smallest value for b is required,
hence b = 2.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• b is a solution of the given equation if and only if b has 0 in all positions where a has 1 (in binary notation).
• So, we need to determine the bit of b for positions where a has 0. Let, if a = 10100001 then the last eight digits of b must be b = 0*0****0, where ‘*’ denotes either 0 or 1. Any replacement of all ‘*’ by 0 or 1 gives us a solution.
• The k-th smallest number will be received by replacing all ‘*’ in y by digits of binary representation of number k.
• As maximum value of a and k is , so checking upto 32 positions in binary representation is enough to get the correct answer for the given equation.

Below is the implementation of above Approach:

## CPP

 `// C++ program to find k'th smallest value for b ` `// such that a + b = a | b ` ` `  `#include ` `using` `namespace` `std; ` ` `  `#define ll long long ` ` `  `// Function to find ` `// the kth smallest value for b ` `ll kthSmallest(ll a, ll k) ` `{ ` ` `  `    ``// res will store final answer ` `    ``ll res = 0; ` `    ``ll j = 0; ` `    ``for` `(ll i = 0; i < 32; i++) { ` ` `  `        ``// skip when j'th position ` `        ``// has 1 in binary representation ` `        ``// as in res, j'th position will be 0. ` ` `  `        ``while` `(j < 32 && (a & (1 << j))) ` `            ``// j'th bit is set ` `            ``j++; ` ` `  `        ``// if i'th bit of k is 1 ` `        ``// and i'th bit of j is 0 ` `        ``// then set i'th bit in res. ` ` `  `        ``if` `(k & (1 << i)) ``// i'th bit is set ` `            ``res |= (1LL << j); ` ` `  `        ``// proceed to next bit ` `        ``j++; ` `    ``} ` `    ``return` `res; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` ` `  `    ``ll a = 10, k = 3; ` ` `  `    ``cout << kthSmallest(a, k) << ``"\n"``; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find k'th smallest value for b ` `// such that a + b = a | b ` `class` `GFG ` `{ ` ` `  `    ``// Function to find ` `    ``// the kth smallest value for b ` `    ``static` `int` `kthSmallest(``int` `a, ``int` `k)  ` `    ``{ ` ` `  `        ``// res wiint store final answer ` `        ``int` `res = ``0``; ` `        ``int` `j = ``0``; ` `        ``for` `(``int` `i = ``0``; i < ``32``; i++) ` `        ``{ ` ` `  `            ``// skip when j'th position ` `            ``// has 1 in binary representation ` `            ``// as in res, j'th position wiint be 0. ` `            ``while` `(j < ``32` `&& (a & (``1` `<< j)) > ``0``) ` `                 `  `                ``// j'th bit is set ` `                ``j++; ` ` `  `            ``// if i'th bit of k is 1 ` `            ``// and i'th bit of j is 0 ` `            ``// then set i'th bit in res. ` `            ``if` `((k & (``1` `<< i)) > ``0``) ``// i'th bit is set ` `                ``res |= (``1` `<< j); ` ` `  `            ``// proceed to next bit ` `            ``j++; ` `        ``} ` `        ``return` `res; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``int` `a = ``10``, k = ``3``; ` ` `  `        ``System.out.print(kthSmallest(a, k) + ``"\n"``); ` `    ``} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## Python

 `# Python3 program to find k'th smallest value for b ` `# such that a + b = a | b ` ` `  `# Function to find ` `# the kth smallest value for b ` `def` `kthSmallest(a, k): ` ` `  `    ``# res wistore final answer ` `    ``res ``=` `0` `    ``j ``=` `0` `    ``for` `i ``in` `range``(``32``): ` ` `  `        ``# skip when j'th position ` `        ``# has 1 in binary representation ` `        ``# as in res, j'th position wibe 0. ` `        ``while` `(j < ``32` `and` `(a & (``1` `<< j))): ` `             `  `            ``# j'th bit is set ` `            ``j ``+``=` `1` ` `  `        ``# if i'th bit of k is 1 ` `        ``# and i'th bit of j is 0 ` `        ``# then set i'th bit in res. ` ` `  `        ``if` `(k & (``1` `<< i)): ``# i'th bit is set ` `            ``res |``=` `(``1` `<< j) ` ` `  `        ``# proceed to next bit ` `        ``j ``+``=` `1` `    ``return` `res ` ` `  `# Driver Code ` ` `  `a ``=` `10` `k ``=` `3` ` `  `print``(kthSmallest(a, k)) ` ` `  `# This code is contributed by mohit kumar 29 `

## C#

 `// C# program to find k'th smallest value for b ` `// such that a + b = a | b ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `    ``// Function to find ` `    ``// the kth smallest value for b ` `    ``static` `int` `kthSmallest(``int` `a, ``int` `k)  ` `    ``{ ` ` `  `        ``// res wiint store final answer ` `        ``int` `res = 0; ` `        ``int` `j = 0; ` `        ``for` `(``int` `i = 0; i < 32; i++) ` `        ``{ ` ` `  `            ``// skip when j'th position ` `            ``// has 1 in binary representation ` `            ``// as in res, j'th position wiint be 0. ` `            ``while` `(j < 32 && (a & (1 << j)) > 0) ` `                 `  `                ``// j'th bit is set ` `                ``j++; ` ` `  `            ``// if i'th bit of k is 1 ` `            ``// and i'th bit of j is 0 ` `            ``// then set i'th bit in res. ` `            ``if` `((k & (1 << i)) > 0) ``// i'th bit is set ` `                ``res |= (1 << j); ` ` `  `            ``// proceed to next bit ` `            ``j++; ` `        ``} ` `        ``return` `res; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main()  ` `    ``{ ` `        ``int` `a = 10, k = 3; ` ` `  `        ``Console.WriteLine(kthSmallest(a, k)); ` `    ``} ` `} ` ` `  `// This code is contributed by AnkitRai01 `

Output:

```5
```

Time Complexity: O(N)

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