Selecting Rows With Sums Equal To A Given Number

You are given say a pricelist of books. And you have to find out
all possible sets of books, each of them having total sum of book
prices equal to a given number.

set nocount on
if object_id('tempdb..#t')>0 drop table #t
if object_id('tempdb..#tt')>0 drop table #tt
create table #t (n int, price int)
insert into #t -- note asc order of book prices
select 1, 1 union all
select 2, 3 union all
select 3, 4 union all
select 4, 5 union all
select 5, 7 union all
select 6, 7 union all
select 7, 11 union all
select 8, 15 union all
select 9, 20 union all
select 10, 20 union all
select 11, 22 union all
select 12, 28 union all
select 13, 33 union all
select 14, 40 union all
select 15, 43 union all
select 16, 47 union all
select 17, 50 union all
select 18, 55 union all
select 19, 56 union all
select 20, 63
go
create table #tt (n int, price int)
go
declare @rows int, @p int, @sum int set @sum=16
delete from #t where price>@sum
set @p=(select sum(price) from #t)

if @p>=@sum
begin
set @rows=(select max(n) from #t)
declare @n int, @s int
set @n=@rows+1 set @s=0

while 0=0
begin
while @n>1
begin
set @n=@n-1
if @s+(select price from #t where n=@n)<=@sum
and @s+(select sum(price) from #t where n<=@n)>=@sum
begin
set @s=@s+(select price from #t where n=@n)
insert into #tt select n, price from #t where n=@n
if @s=@sum select * from #tt --- outputting
end
end
set @n=(select min(n) from #tt)
set @s=@s-(select price from #tt where n=@n)
delete from #tt where n=@n
if @s=0 and (select sum(price) from #t where n<@n)<@sum break
end

end
drop table #tt
drop table #t

Result for @sum=16 (for e.g. @sum=76 number of different sets = 196):
n price
----------- -----------
8 15
1 1

n price
----------- -----------
7 11
4 5

n price
----------- -----------
7 11
3 4
1 1

n price
----------- -----------
6 7
4 5
3 4

n price
----------- -----------
6 7
4 5
2 3
1 1

n price
----------- -----------
5 7
4 5
3 4

n price
----------- -----------
5 7
4 5
2 3
1 1
EDIT: added one more condition (in blue) into an IF statement.
Now it works incredibly fast.