Split components of a symbolic vector into positive and negative

Given a symbolic expression I would like to split the positive and negative terms and further split if the coefficients are not 1. I would like to obtain a vector whose components are the positive terms and another vector whose components are the negative terms of the expression.

Let me illustrate with an example:

Variables x1 x2 y1 y2

Given X=x1^2*y2^5 - 2*y1^2*x1*x2+ 3*x1 -y2

I would like to obtain two vector Vp=[x1^2*y2, x1, x1, x1] (notice that x1 appears 3 times since the coefficient in front of x1 is 3) Vn=[y1^2*x1*x2, y1^2*x1*x2, y2] (notice that y1^2*x1*x2 appears 2 times since the coefficient in front of y1^2*x1*x2 is -2)

I do not care about the specific order of the elements in each vector.

I know how to separate positive and negative components but not split the coefficients further. I would obtain something like this instead:

Vp=[x1^2*y2, 3*x1] Vn=[2*y1^2*x1*x2, y2]

Answer 1

[Azzi Abdelmalek]

syms x1 x2 y1 y2
X=x1^2*y2^5 - 2*y1^2*x1*x2+ 3*x1 -y2
[s1,s2]=coeffs(X,[x1,x2,y1,y2]);
idxp=s1>0;
Xp1=s2(idxp);
Xn1=s2(~idxp);
ip=s1(idxp);
in=s1(~idxp)
Vp=[];
Vn=[];
for k=1:numel(Xp1)
  Vp=[Vp repmat(Xp1(k),1,ip(k))];
end
for k=1:numel(Xn1)
  Vn=[Vn repmat(Xn1(k),1,abs(in(k)))];
end
Vp
Vn