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.




sub eq_index {
    my ( $i, $sum, %sums ) = ( 0, 0 );
 
    for (@_) {
        push @{ $sums{ $sum * 2 + $_  } }, $i++;
        $sum += $_;
    }
 
    return join ' ', @{ $sums{$sum} || [] }, "\n";
}
 
print eq_index qw(  -7  1  5  2 -4  3  0 ); # 3 6
print eq_index qw(   2  4  6             ); # (no eq point)
print eq_index qw(   2  9  2             ); # 1
print eq_index qw(   1 -1  1 -1  1 -1  1 ); # 0 1 2 3 4 5 6