Question: If Mikhail goes from the point $(x1, y1)$ to the point $(x2, y2)$ in one move, and $x1 \ne x2$ and $y1 \ne y2$, then such a move is called a diagonal move. Mikhail has $q$ queries. For the $i$-th query Mikhail's target is to go to the point $(n_i, m_i)$ from the point $(0, 0)$ in exactly $k_i$ moves. Among all possible movements he want to choose one with the maximum number of diagonal moves. Your task is to find the maximum number of diagonal moves or find that it is impossible to go from the point $(0, 0)$ to the point $(n_i, m_i)$ in $k_i$ moves. Note that Mikhail can visit any point any number of times (even the destination point!).

Output:

Let's break down this problem step-by-step.

Understanding the Problem

Mikhail's Moves: Mikhail can move diagonally, meaning he can move in a way that forms a diagonal line between two points.
Queries: Mikhail has a set of queries, each representing a target point.
Target Point: The target point is the point Mikhail wants to reach.
Moves: The number of moves Mikhail needs to make to reach the target point.
Diagonal Moves: The maximum number of diagonal moves Mikhail can make.

Analyzing the Problem

The problem is about finding the maximum number of diagonal moves Mikhail can make to reach a target point.

Key Concepts

Diagonal Movement: Mikhail can move diagonally, meaning he can move in a way that forms a diagonal line between two points.
Distance: The distance between two points is important to determine the number of moves.

Solution Approach

Understanding the Constraints: The problem provides information about the starting point, the target point, and the number of queries.
Analyzing the Queries: The queries are the starting points for Mikhail's movements.
Finding the Maximum Number of Diagonal Moves: The maximum number of diagonal moves Mikhail can make is the maximum number of diagonal moves he can make to reach the target point.

Code Example (Python)

python

def find_max_diagonal_moves(queries, queries_index):
    # ... (Implementation of the logic to find the maximum number of diagonal moves)

# ... (Implementation of the logic to find the maximum number of diagonal moves)

Important Notes

Implementation: The code example is a starting point. You'll need to implement the logic to find the maximum number of diagonal moves.
Constraints: The problem provides information about the starting point, the target point, and the number of queries.
Constraints: The problem provides information about the starting point, the target point, and the number of queries.

Let me know if you have any other questions.

Prompt: 149 tokens, 386.395 tokens-per-sec Generation: 460 tokens, 24.677 tokens-per-sec Peak memory: 5.358 GB

MCES10/code-gen-gemma-2-2b-it

Code Generation and Problem Solving

Google's Gemma 2 2b it

Fine Tuned on Kaggle Dataset https://www.kaggle.com/datasets/thedevastator/coding-questions-with-solutions

Text Generation

Input:

Output:

Let me know if you have any other questions.

MCES10/
code-gen-gemma-2-2b-it