Kernel of an algebra homomorphism.

Question

Let $A$ be a commutative $\mathbb{K}$-algebra generated by the monomials $x^m, x^{m-1}y, x^{m-2}y^2,\cdots,y^m$ where $x$ and $y$ commutes. This implies the generators are not algebraically independent. So the algebra is not isomorphic to the polynomial algebra generated by these monomials. But it must be isomorphic to a quotient of the polynomial algebra $\mathbb{K}[x^m, x^{m-1}y, x^{m-2}y^2,\cdots,y^m]$. Can anyone help me to find out the ideal by which I need to quotient the polynomial algebra. Obviously there are few relations that can be obtained but I am not getting any idea to specifically find out the ideal.