An AI research team is extending the context window for two different language models, Model A and Model B. Both models need to be scaled from an original length of 2048 tokens to a new length of 8192 tokens. The only difference between them is their embedding dimensionality (d):

• Model A: d = 64
• Model B: d = 512

The team will use the formula below to calculate the required scaling factor (λ):

$\lambda = \left(\frac{m}{m_l}\right)^{\frac{d}{d-2}}$

Without performing the full calculation, predict which model will require a larger scaling factor (λ). Justify your reasoning by analyzing how the embedding dimensionality (d) influences the exponent in the formula.