How to replace a certain value across a list of dataframe columns with random values efficiently?

I have a dataframe (a very large one) that looks as follows:

For the sake of completeness, here is a screenshot containing a larger cutout of this dataframe:

How can we replace all ones (all values 1) within the columns a_1 to a_1000 each with a random value other than 0, 1 and 2?

What I tried so far works but seems not to be elegant:

cols = ["a_" + str(i) for i in range(1, 1000+1)]

for col in cols:
    df[col] = df[col].apply(lambda x: random.choice(range(3, 20)) if x == 1 else x)
df.head()

I would be greatful for any hint to implement this in a more staright-forward manner.
Note df[cols].apply(...) does not work, since it yields an error "ValueError: The truth value of a Series is ambiguous. Use a.empty, a.bool(), a.item(), a.any() or a.all()."

>Solution :

IIUC, you can use:

cols = df.filter(like='a_').columns

df[cols] = df.mask(df[cols].eq(1),
                   np.random.randint(3,1000,(df.shape[0], len(cols))))

reproducible example:

np.random.seed(0)
df = pd.DataFrame(np.random.randint(0, 10, (10,10)),
                  columns=[f'a_{i+1}' for i in range(10)])

output:

   a_1  a_2  a_3  a_4  a_5  a_6  a_7  a_8  a_9  a_10
0    5    0    3    3    7    9    3    5    2     4
1    7    6    8    8  957    6    7    7    8   380
2    5    9    8    9    4    3    0    3    5     0
3    2    3    8  785    3    3    3    7    0    89
4    9    9    0    4    7    3    2    7    2     0
5    0    4    5    5    6    8    4  592    4     9
6    8  773  518    7    9    9    3    6    7     2
7    0    3    5    9    4    4    6    4    4     3
8    4    4    8    4    3    7    5    5    0   846
9    5    9    3    0    5    0   28    2    4     2