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.




package main
 
import (
    "fmt"
    "math/rand"
    "time"
)
 
func main() {
    fmt.Println(ex([]int32{-7, 1, 5, 2, -4, 3, 0}))
 
    // sequence of 1,000,000 random numbers, with values
    // chosen so that it will be likely to have a couple
    // of equalibrium indexes.
    rand.Seed(time.Now().UnixNano())
    verylong := make([]int32, 1e6)
    for i := range verylong {
        verylong[i] = rand.Int31n(1001) - 500
    }
    fmt.Println(ex(verylong))
}
 
func ex(s []int32) (eq []int) {
    var r, l int64
    for _, el := range s {
        r += int64(el)
    }
    for i, el := range s {
        r -= int64(el)
        if l == r {
            eq = append(eq, i)
        }
        l += int64(el)
    }
    return
}