Unique values in two columns - sql-server

Question

I have two columns and I need them both to be unique between each other (like it is 1 column).
My first attempt was to create sequence and set default constraints.
create sequence seq1
as bigint
start with 1
increment by 1
cache;
go
create table product (
pk uniqueidentifier
, id_1 bigint not null default (next value for seq1)
, id_2 bigint not null default (next value for seq1)
);
go
insert into product (pk) values (newid());
insert into product (pk) values (newid());
insert into product (pk) values (newid());
insert into product (pk) values (newid());
insert into product (pk) values (newid());
go
And it doesn't work. The result of query above will be:
id_1 id_2
1 1
2 2
3 3
4 4
5 5
Currently I stopped using 2 sequences with even and not even numbers.
create sequence seq2
as bigint
start with 1
increment by 2
cache;
go
create sequence seq3
as bigint
start with 2
increment by 2
cache;
go
But if in future I will need to add another column which also must be unique I will have a problem.
I also thinked about stored procedures. Something like this works for me.
create procedure sp_insertProduct
as
begin
declare #id1 as bigint = next value for seq1;
declare #id2 as bigint = next value for seq1;
insert into product (pk, id_1, id_2) values (newid(), #id1, #id2);
end
go
exec sp_insertProduct;
exec sp_insertProduct;
exec sp_insertProduct;
go
But due to my ORM framework restictions I cannot use stored procedures for inserting.
So is there a better solution for that problem?
PS. for some reasons I can not use uniqueidentifiers.
UPDATE
I think I need to explain question a bit clearly. I have a working solution for now (and both current answers will also work), but I wonder if there is a extensible solution to:
provide uniqueness of values in multiple columns (with ability to
add additional columns in future).
avoid using uniqueidentifiers
for better understanding of question, this is how I check uniqueness:
with src as (
select id_1 as id from product
union all
select id_2 as id from product
)
select id, count(*) as equal_values
from src
group by id
having (count(*) > 1)

Answer 1

create sequence seq1
as bigint
start with 1
increment by 2
cache;
go
create table product (
pk uniqueidentifier
, id_1 bigint not null default (next value for seq1)
, id_2 bigint not null default (next value for seq1 + 1)
);
go
doing this..
insert into product (pk) values (newid());
insert into product (pk) values (newid());
insert into product (pk) values (newid());
insert into product (pk) values (newid());
insert into product (pk) values (newid());
this would generate..
pk id_1 id_2
2A159914-8105-4DC1-9D7E-570CC5444172 1 2
6DAFEF16-2B81-4A10-99EF-B3F1A74389C6 3 4
8C6F6697-D993-4320-92BB-04CD56804C5A 5 6
AC97F37F-CAC3-4E83-BDD4-4B55D009C334 7 8
3DDAADA0-D7DB-4350-8087-ABF02B539552 9 10
SQL Fiddle

Answer 2

May be this seems very naive but it should work. I didn't check but you may need to add some parenthesis:
create table product (
pk uniqueidentifier
, id_1 bigint not null default (next value for seq1)
, id_2 bigint not null default (-next value for seq1)
);
go