THE TOKEN BUDGET GATE

Difficulty: Medium Tags: LLM Inference, Context Windows, Memory Accounting

Story

A hosted language-model API must admit requests only when the prompt and reserved generation tokens fit the model's context window. An off-by-one error accepts a request that exceeds the supported sequence length.

The Math

Let P be the prompt-token count, R the requested generation-token count, and C the context limit. A request fits exactly when:

P + R <= C

The maximum generation budget still available for this prompt is:

R_max = max(0, C - P)

Input Format

P, R, C (non-negative integers).

Output Format

R_max, then whether the request fits (True/False).

Constraints

• 0 <= P, R, C <= 10^18.
• Time limit: 1.0 second. Memory: 64 MB.

Example

Input

P = 7900, R = 300, C = 8192

Output

292 NO

Explanation: The prompt leaves 8192 - 7900 = 292 positions. A request for 300 tokens exceeds the limit by 8.