#B4261. Finding Minimal y for Bitwise Equation
Finding Minimal y for Bitwise Equation
Finding Minimal y for Bitwise Equation
Given an integer \(x\), find the smallest positive integer \(y\) such that the following equation holds:
\[ (x \ \operatorname{and} \ y) + (x \ \operatorname{or} \ y) = 2025 \]
Here, \(\operatorname{and}\) denotes the bitwise AND operation and \(\operatorname{or}\) denotes the bitwise OR operation. If no such positive integer \(y\) exists, output \(-1\).
Note: It can be verified that for any two integers \(x\) and \(y\), the identity \((x \ \operatorname{and} \ y) + (x \ \operatorname{or} \ y) = x + y\) holds. Hence, the problem reduces to finding the smallest positive integer \(y\) such that \(x + y = 2025\), meaning \(y = 2025 - x\) when \(2025 - x > 0\).
inputFormat
The input consists of a single integer \(x\).
Format: A single line containing one integer \(x\).
outputFormat
Output the smallest positive integer \(y\) such that \(x + y = 2025\). If no such \(y\) exists (i.e. if \(2025 - x \le 0\)), output \(-1\).
sample
1000
1025