[Python] Compare 2 tables in Polars and select a value based on that comparison

I have a table like this in polars:

df_a = pl.from_repr("""
┌─────────────────────┬───────┐
│ arrival_time ┆ Train │
│ --- ┆ --- │
│ datetime[ns] ┆ i64 │
╞═════════════════════╪═══════╡
│ 2024-10-04 08:40:10 ┆ 112 │
│ 2024-10-04 19:31:26 ┆ 134 │
└─────────────────────┴───────┘
""")


An I have another table that defines the period of the day based on the hours:

df_b = pl.from_repr("""
┌─────────────────────┬───────────┐
│ Time ┆ Period │
│ --- ┆ --- │
│ datetime[ns] ┆ str │
╞═════════════════════╪═══════════╡
│ 2024-10-04 08:00:00 ┆ Early │
│ 2024-10-04 16:00:00 ┆ Afternoon │
└─────────────────────┴───────────┘
""")


What I am trying to achieve is a Polars way to combine both tables and obtain in the first table the Period of the day as a new column:

┌─────────────────────┬───────┬───────────┐
│ arrival_time ┆ Train ┆ Period │
│ --- ┆ --- ┆ --- │
│ datetime[ns] ┆ i64 ┆ str │
╞═════════════════════╪═══════╪═══════════╡
│ 2024-10-04 08:40:10 ┆ 112 ┆ Early │
│ 2024-10-04 19:31:26 ┆ 134 ┆ Afternoon │
└─────────────────────┴───────┴───────────┘


For now what I am doing is working entirely with dictionaries, zipping the 2 columns of my comparison table and computing the key of the minimium distance beetween the 2 time columns:

min(dict(zip( df.Period,df.Time)).items(), key=lambda x: abs(pl.col('arrival_time') - x[1]))[0])


But i am certainly sure that there's a better way to process in Polars.

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