Source code must be written in R5RS!

Write a function two-subsets in Scheme that takes a list L of positive integers (duplicates are possible, zero is not considered a positive integer) and some auxiliary parameters of your choice. The function two-subsets returns #t if the list L contains two subsets with equal sums of elements and with equal numbers of elements. Otherwise (if two subsets satisfying the condition above do not exist), the function returns #f. Assume that the list L contains at least two integers.

It is up to you to choose the auxiliary parameters that two-subsets takes. All auxiliary parameters must be numeric (not lists) and should have initial values set to zero. For example, if L is (1 2 3) and if you decide to use two additional auxiliary parameters, then two-subsets must be called as follows:

(two-subsets '(1 2 3) 0 0)

If there are three auxiliary parameters, then the function must be called: (two-subsets '(1 2 3) 0 0 0) and so on.

Examples:

(two-subsets '(7 7) 0 0) returns #t. The two subsets are {7} and {7}.

(two-subsets '(5 3 2 4) 0 0) returns #t. The two subsets are {2, 5} and {3, 4}.

(two-subsets '(1 2 3 6 9) 0 0) returns #f.

The whole solution must be packed in one recursive function two-subsets which must look as follows:

(define two-subsets (lambda (

of your choice initially set to zero>)

(cond

... )))

In other words, you have to choose your auxiliary parameters and define a COND statement. Nested COND statements are allowed.

Inside COND, you can use ONLY the following constructs:

-null?

-cond

-car

-cdr

-else

-+

-=

- not

- and

- #t

- #f

- two-subsets

- the names of your parameters, such as list, sum, etc. - numeric constants, such as 0, 1, 2, etc.

- parentheses

You cannot use a construct if it is not listed above. In other words, your code must define and use only one function, two-subsets, which must be defined using the template and the constructs listed above. The use of built-in functions is not allowed.