A developer is debugging a text-generation model. The model is given an initial input sequence x = "The recipe calls for two cups of". The developer logs the model's state, which is defined as a pair containing the initial input and the sequence of tokens generated so far, at two consecutive time steps, t=1 and t=2.

• State at t=1: (x, y_1) where y_1 = "flour"
• State at t=2: (x, y_2) where y_2 = "flour and"

Based on the provided logs, analyze the change in the model's state from time step t=1 to t=2. Explain which component of the state was updated and why this update is essential for the model to predict the next token at t=3.