Can you suggest a method to generate random sample from following PDF?

Question

‎Let‎ ${‎‎\bf{\alpha}}=(\alpha_1, \alpha_2, \ldots, \alpha_m)$ ‎and ‎‎$‎‎\textbf{b}=(b_1, b_2, \ldots, b_m, b_{m+1}).$ I intend ‎to ‎generate ‎sample ‎from PDF $$ g(\alpha_1, \alpha_2, \ldots, \alpha_m)=Const. ‎\frac{(1+\sum_{i=1}^{m}\alpha_i)^{m+1}}{\prod_{j=1}^{2}(\sum_{i=1}^{m}\alpha_ic_i+d_j)^{a_j}}‎‎\times f_{Dirichlet}({\bf{\alpha}}) , ‎~~~\alpha_i, c_i, d_j, ‎a_j>0‎ $$ where ‎$‎f_{Dirichlet}‎$ ‎is ‎the ‎PDF ‎of ‎Dirichlet ‎Type-II ‎distribution, i.e.‎ $$ ‎f_{Dirichlet}({\bf{\alpha}})=‎\frac{\Gamma(\sum_{i=1}^{m+1}b_i) \prod_{i=1}^{m}\alpha_i^{b_i-1}}{\prod_{i=1}^{m+1}\Gamma(b_i)(1+\sum_{i=1}^{m}\alpha_i)^{\sum_{i=1}^{m+1}b_i}}‎~~~b_i>0. $$ I think the Metropolis-Hastings (MH) algorithm is useful. But I don't know how to choose a suitable jump distribution for choosing candidate values. What is your idea?‎