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.




 
# syntax: GAWK -f EQUILIBRIUM_INDEX.AWK
BEGIN {
    main("-7 1 5 2 -4 3 0")
    main("2 4 6")
    main("2 9 2")
    main("1 -1 1 -1 1 -1 1")
    exit(0)
}
function main(numbers,  x) {
    x = equilibrium(numbers)
    printf("numbers: %s\n",numbers)
    printf("indices: %s\n\n",length(x)==0?"none":x)
}
function equilibrium(numbers,  arr,i,leftsum,leng,str,sum) {
    leng = split(numbers,arr," ")
    for (i=1; i<=leng; i++) {
      sum += arr[i]
    }
    for (i=1; i<=leng; i++) {
      sum -= arr[i]
      if (leftsum == sum) {
        str = str i " "
      }
      leftsum += arr[i]
    }
    return(str)
}
 