Shopping in Mars is quite a different experience. The Mars people pay
by chained diamonds. Each diamond has a value (in Mars dollars M$).
When making the payment, the chain can be cut at any position for only
once and some of the diamonds are taken off the chain one by one. Once
a diamond is off the chain, it cannot be taken back. For example, if we
have a chain of 8 diamonds with values M$3, 2, 1, 5, 4, 6, 8, 7, and we
must pay M$15. We may have 3 options:
1. Cut the chain between 4 and 6, and take off the diamonds from the
position 1 to 5 (with values 3+2+1+5+4=15).
2. Cut before 5 or after 6, and take off the diamonds from the position
4 to 6 (with values 5+4+6=15).
3. Cut before 8, and take off the diamonds from the position 7 to 8
(with values 8+7=15).
Now given the chain of diamond values and the amount that a customer
has to pay, you are supposed to list all the paying options for the customer.
If it is impossible to pay the exact amount, you must suggest solutions
with minimum lost.