Bonus for p315

We define a needle-like primitive convex quadrilateral as follows:

It has 4 vertices on lattice points

It has no other lattice points inside or onside

Find such a quadrilateral with the maximum possible perimeter in x² + y² = R² circle for R=10⁸? Answer format: x₁,y₁,x₂,y₂ where |x_i| ≥ |y_i| and x₁ < x₂ (See the example below) Example: 3,2,5,3 if R = 5 There are more than one solutions. Enter the two vectors that identify them. For example A(-4,-3); B(-1,-1); C(4,2); D(1,0) is a solution then the two vectors are AB=DC=[3,2] and BC=AD=[5,3] Similarly, for A(-4,-2); B(-1,0); C(4,3); D(1,1) AB=DC=[3,2] and BC=AD=[5,3] [My timing: 30s]