calculate cumulative sum over month and by group as well

I first calculated monthly sum by counting IDs within a group using group-by and mutate. However, as I try to use cumsum to calculate monthly cumulative sum by group using cumsum, the data just does not look right. It would be really helpful if someone can help me. Thanks~

Assuming original data frame looks like so:

I would like to have a final output data frame like the one below.

Only summing the first group value

library(dplyr)

df %>% 
  mutate(monthlySum = n_distinct(person.id), 
         cumulativeSum = row_number() == 1, .by = c(company, yyyy, month)) %>% 
  mutate(cumulativeSum = cumsum(if_else(cumulativeSum, monthlySum, 0)), 
    .by =c(company, yyyy))
   person.id company yyyy    month monthlySum cumulativeSum
1          1       A 2011  January          2             2
2          2       A 2011  January          2             2
3          3       A 2011 Feburary          3             5
4          4       A 2011 Feburary          3             5
5          5       A 2011 Feburary          3             5
6          6       A 2011    March          1             6
7          7       B 2011  January          3             3
8          8       B 2011  January          3             3
9          9       B 2011  January          3             3
10        10       B 2011 Feburary          4             7
11        11       B 2011 Feburary          4             7
12        12       B 2011 Feburary          4             7
13        13       B 2011 Feburary          4             7
14        14       B 2011    March          2             9
15        15       B 2011    March          2             9
16        16       B 2011    April          1            10