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.




// version 1.1
 
fun equilibriumIndices(a: IntArray): MutableList<Int> {
   val ei = mutableListOf<Int>()
   if (a.isEmpty()) return ei // empty list
   val sumAll  = a.sumBy { it }
   var sumLeft = 0
   var sumRight: Int
   for (i in 0 until a.size) {
       sumRight = sumAll - sumLeft - a[i]
       if (sumLeft == sumRight) ei.add(i)
       sumLeft += a[i]
   }
   return ei
}
 
fun main(args: Array<String>) {
    val a = intArrayOf(-7, 1, 5, 2, -4, 3, 0)
    val ei = equilibriumIndices(a)
    when (ei.size) {
         0     -> println("There are no equilibrium indices")
         1     -> println("The only equilibrium index is : ${ei[0]}")
         else  -> println("The equilibrium indices are : ${ei.joinToString(", ")}")
    }
}