An equilibrium index of a sequence is an index into the sequence such that the sum of elements at lower indices is equal to the sum of elements at higher indices.



For example, in a sequence   



A


{\displaystyle A}

:

   




A

0


=
−
7


{\displaystyle A_{0}=-7}


   




A

1


=
1


{\displaystyle A_{1}=1}


   




A

2


=
5


{\displaystyle A_{2}=5}


   




A

3


=
2


{\displaystyle A_{3}=2}


   




A

4


=
−
4


{\displaystyle A_{4}=-4}


   




A

5


=
3


{\displaystyle A_{5}=3}


   




A

6


=
0


{\displaystyle A_{6}=0}


3   is an equilibrium index, because:

   




A

0


+

A

1


+

A

2


=

A

4


+

A

5


+

A

6




{\displaystyle A_{0}+A_{1}+A_{2}=A_{4}+A_{5}+A_{6}}


6   is also an equilibrium index, because:

   




A

0


+

A

1


+

A

2


+

A

3


+

A

4


+

A

5


=
0


{\displaystyle A_{0}+A_{1}+A_{2}+A_{3}+A_{4}+A_{5}=0}


(sum of zero elements is zero)

7   is not an equilibrium index, because it is not a valid index of sequence 



A


{\displaystyle A}

.



Task;
Write a function that, given a sequence, returns its equilibrium indices (if any).

Assume that the sequence may be very long.




procedure main(arglist)
L := if *arglist > 0 then arglist else [-7, 1, 5, 2, -4, 3, 0]   # command line args or default
every writes( "equilibrium indicies of [ " | (!L ||" ") | "] = " | (eqindex(L)||" ") | "\n" )
end
 
procedure eqindex(L) # generate equilibrium points in a list L or fail
local s,l,i
 
every (s := 0, i := !L) do
   s +:= numeric(i) | fail              # sum and validate
 
every (l := 0, i := 1 to *L) do {
   if l = (s-L[i])/2 then suspend i     
   l +:= L[i]                           # sum of left side
   }
end