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.




MODE YIELDINT = PROC(INT)VOID;
 
PROC gen equilibrium index = ([]INT arr, YIELDINT yield)VOID:
(
    INT sum := 0;
    FOR i FROM LWB arr TO UPB arr DO
        sum +:= arr[i]
    OD;
 
    INT left:=0, right:=sum;
    FOR i FROM LWB arr TO UPB arr DO
        right -:= arr[i];
        IF left = right THEN yield(i) FI;
        left +:= arr[i]
    OD
);
 
test:(
  []INT arr = []INT(-7, 1, 5, 2, -4, 3, 0)[@0];
# FOR INT index IN # gen equilibrium index(arr, # ) DO ( #
##   (INT index)VOID: 
     print(index)
# OD # );
  print(new line)
)