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.




import math, sequtils, strutils
 
iterator eqindex(data: openArray[int]): int =
  var suml, ddelayed = 0
  var sumr = sum(data)
  for i,d in data:
    suml += ddelayed
    sumr -= d
    ddelayed = d
    if suml == sumr:
      yield i
 
const d = @[@[-7, 1, 5, 2, -4, 3, 0],
            @[2, 4, 6],
            @[2, 9, 2],
            @[1, -1, 1, -1, 1, -1, 1]]
 
for data in d:
  echo "d = [", data.join(", "), ']'
  echo "eqIndex(d) -> [", toSeq(eqindex(data)).join(", "), ']'