Extra dimension on first argument passed into apply_ufunc

Here's my code:

import numpy as np
import xarray as xr

da = xr.DataArray(np.random.rand(1000, 100))
da = da.rename({'dim_0': 'rows_a'})
db = xr.DataArray(np.random.rand(1000, 100))
db = db.rename({'dim_0': 'rows_b'})

def print_shape(a):
    print(a.shape)
    return np.zeros(shape=(a.shape[0]))

def print_two_shapes(a, b):
    print(a.shape)
    print(b.shape)
    return np.zeros(shape=(a.shape[0], b.shape[0]))

If I print_shape and print_shapes with apply_ufunc I am surprised by the results:

xr.apply_ufunc(
    print_shape,
    da,
    input_core_dims=[['dim_1']]
)

(1000, 100)
<xarray.DataArray (rows_a: 1000)>
array([0., 0., 0., ..., 0., 0., 0.])
Coordinates:
  * rows_a   (rows_a) int64 0 1 2 3 4 5 6 7 ... 992 993 994 995 996 997 998 999

vs

xr.apply_ufunc(
    print_two_shapes,
    da, db,
    input_core_dims=[['dim_1'], ['dim_1']]
)

(1000, 1, 100)
(1000, 100)

<xarray.DataArray (rows_a: 1000, rows_b: 1000)>
array([[0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.],
       ...,
       [0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.],
       [0., 0., 0., ..., 0., 0., 0.]])
Coordinates:
  * rows_a   (rows_a) int64 0 1 2 3 4 5 6 7 ... 992 993 994 995 996 997 998 999
  * rows_b   (rows_b) int64 0 1 2 3 4 5 6 7 ... 992 993 994 995 996 997 998 999

My array da has changed shape from (1000, 100) to (1000, 1, 100) when a second argument was added to my call to apply_ufunc.

Maybe this is documented, but I missed it. If it is documented I'd be glad to be pointed to it and I'll see if I can come up with a suggestion of how to highlight this better in the documentation as it really threw me.

Start by reproducing the two apply_ufunc calls using the Python, NumPy, and xarray example in the issue, focusing on input_core_dims and the differing argument counts. Read the apply_ufunc documentation and clarify why the first argument receives different shapes; done means the documented behavior explains both printed results and how to avoid the surprise.