Use CTE and Window Function to get the number of hiring under a budget

I have a table candidates in which there are three columns id, position, and salary.

The code to generate the table is

create table candidates (
id int primary key,
position varchar not null,
salary int not null
);
insert into candidates values (1, 'junior', 10500);
insert into candidates values (2, 'senior', 15000);
insert into candidates values (3, 'senior', 35000);
insert into candidates values (4, 'junior', 8000);
insert into candidates values (5, 'senior', 30000);
insert into candidates values (6, 'senior', 25000);
insert into candidates values (7, 'junior', 30000);
insert into candidates values (8, 'senior', 50000);
insert into candidates values (9, 'senior', 30000);
insert into candidates values (10, 'junior', 7000);
insert into candidates values (11, 'junior', 8000);
insert into candidates values (12, 'senior', 33000);
insert into candidates values (13, 'junior', 5000);
insert into candidates values (14, 'senior', 47000);
insert into candidates values (15, 'junior', 12000);

I have a budget of 150000 and I need to hire as many low-cost seniors as possible, and with the remaining money, I can hire as many juniors as possible. I wrote this code to get the cumulative sum of money for seniors and juniors.

SELECT id, position, salary, SUM(salary) OVER (PARTITION BY position ORDER BY salary) AS cum_salary
FROM candidates
ORDER BY position DESC, salary;

The output I get is

I can see that I can use 133000 (which is less than 150000) to hire 5 seniors and use the rest of the money (150000 - 133000 = 17000) to hire two juniors. So, the final output should be something like

How can I write this query using CTE and Window Function in POSTGRESQL 9.6 to get the kind of output I need for larger datasets, where it will not always be possible to do it manually?

PS: I am not an expert user of Postgres 9.6.

This would do it:

WITH cte AS (
   SELECT position, salary
        , sum(salary)  OVER w AS cum_salary
        , row_number() OVER w AS count
   FROM   candidates
   WINDOW w AS (PARTITION BY position ORDER BY salary)
   )
, sen AS (
   SELECT position, cum_salary, count
   FROM   cte
   WHERE  position = 'senior'
   AND    cum_salary <= 150000
   ORDER  BY cum_salary DESC
   LIMIT  1
   )
SELECT position, count FROM sen
UNION ALL
(  -- parentheses required
SELECT position, count
FROM   cte
WHERE  position = 'junior'
AND    cum_salary <= (SELECT 150000 - cum_salary FROM sen)
ORDER  BY cum_salary DESC
LIMIT  1
);

db<>fiddle here