[Python] Finding the last row that meets conditions of a mask

This is my dataframe:

df = pd.DataFrame({'a': [20, 21, 333, 444], 'b': [20, 20, 20, 20]})


I want to create column c by using this mask:

mask = (df.a >= df.b)


And I want to get the last row that meets this condition and create column c. The output that I want looks like this:

a b c
0 20 20 NaN
1 21 20 NaN
2 333 20 NaN
3 444 20 x


I tried the code below but it didn't work:

df.loc[mask.cumsum().gt(1) & mask, 'c'] = 'x'

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