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 "/fmt" for Fmt
 
var equilibrium = Fn.new { |a|
    var len = a.count
    var equi = []
    if (len == 0) return equi // sequence has no indices at all
    var rsum = a.reduce { |acc, x| acc + x }
    var lsum = 0
    for (i in 0...len) {
        rsum = rsum - a[i]
        if (rsum == lsum) equi.add(i)
        lsum = lsum + a[i]
    }
    return equi
}
 
var tests = [
    [-7, 1, 5, 2, -4, 3, 0],
    [2, 4, 6],
    [2, 9, 2],
    [1, -1, 1, -1, 1, -1, 1],
    [1],
    []
]
 
System.print("The equilibrium indices for the following sequences are:\n")
for (test in tests) {
    System.print("%(Fmt.s(24, test)) -> %(equilibrium.call(test))")
}