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Existing approaches often rely on sorting, which incurs significant computation and memory overhead on GPUs, or on stochastic approaches that alter the algorithm's output. In this work, we propose Qrita, an efficient Top-k and Top-p algorithm based on a pivot-based truncation and selection. Qrita leverages pivot-based search for both Top-k and Top-p with two key techniques: 1. Gaussian-based sigma-truncation, which greatly reduces the search space of the vocabulary, and 2. Quaternary pivot search with duplication handling, which halves the number of pivot search iterations and guarantees deterministic output. 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