  We show the denominator formulas for the normalized $R$-matrix involving two
arbitrary Kirillov--Reshetikhin (KR) modules $W^{(k)}_{m,a}$ and
$W^{(l)}_{p,b}$ in all nonexceptional affine types, $D_4^{(3)}$, and
$G_2^{(1)}$. To achieve our goal, we prove the existence of homomorphisms,
which can be understood as generalization of Dorey rule to KR modules. We also
conjecture a uniform denominator formulas for all simply-laced types; in
particular, type $E_n^{(1)}$. With the denominator formulas, we determine the
simplicity of tensor product of KR modules and degrees of poles of normalized
$R$-matrices between two KR modules completely in nonexceptional affine types,
$D_4^{(3)}$, and $G_2^{(1)}$. As an application, we prove that the certain sets
of KR modules for the untwisted affine types, suggested by Hernandez and
Leclerc as clusters, form strongly commuting families, which implies that all
cluster monomials in the clusters are real simple modules.
