# Compute nCr naively using UHUGEINT
# The caller should ensure 2r < n
create or replace function nCr_(n, r) as
    (with recursive cte as
      (SELECT 1::UHUGEINT as c, n as numerator, 1::UHUGEINT as m
       UNION ALL
       SELECT (c * numerator / m) as c,
       (numerator - 1) as numerator,
       (m + 1) as m
       FROM cte
       WHERE m <= r)
    SELECT last(c order by m)
    FROM cte
);

create or replace function nCr(n,r) as (
  if( n<r,      error('nCr expects r <= n'),
  if( 2*r <= n, nCr_(n,r),
                nCr_(n, n-r) ) )
);

## Example:
select nCr(140,50);