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.




$ include "seed7_05.s7i";
 
const array integer: numList is [] (-7, 1, 5, 2, -4, 3, 0);
 
const func array integer: equilibriumIndex (in array integer: elements) is func
  result
    var array integer: indexList is 0 times 0;
  local
    var integer: element is 0;
    var integer: index is 0;
    var integer: sum is 0;
    var integer: subSum is 0;
    var integer: count is 0;
  begin
    indexList := length(elements) times 0;
    for element range elements do
      sum +:= element;
    end for;
    for element key index range elements do
      if 2 * subSum + element = sum then
        incr(count);
        indexList[count] := index;
      end if;
      subSum +:= element;
    end for;
    indexList := indexList[.. count];
  end func;
 
const proc: main is func
  local
    var array integer: indexList is 0 times 0;
    var integer: element is 0;
  begin
    indexList := equilibriumIndex(numList);
    write("Found:");
    for element range indexList do
      write(" " <& element);
    end for;
    writeln;
  end func;