\bar{K}$ decays. The large value of $\phi_A^i$, corresponding to a large imaginary part of the enhanced complex corrections, also lends some support to the pQCD claim that the annihilation amplitudes can provide a large strong phase [@pqcd].

There are two possible solutions for the factorizable annihilation parameters, namely, Part A $(\rho_A^f,\phi_A^f)$ $\approx$ $(1.1,-40^{\circ})$ and Part B $(\rho_A^f,\phi_A^f)$ $\approx$ $(2.7,166^{\circ})$. From Fig.\[ParaSpacI\], it can be seen that there is no overlap between the regions of $(\rho_A^f,\phi_A^f)$ and $(\rho_A^i,\phi_A^i)$ at the 95% confidence level, which indicates that it might be wrong to treat $(\rho_A^f,\phi_A^f)$ $=$ $(\rho_A^i,\phi_A^i)$ $=$ $(\rho_A,\phi_A)$ as universal parameters for nonfactorizable and factorizable annihilation topologies in pervious studies. Our fit results certify the suggestion of Ref.[@zhu1; @zhu2] that different annihilation topologies should be parameterized by different annihilation parameters, i.e., $(\rho_A^f,\phi_A^f)$ $\neq$ $(\rho_A^i,\phi_A^i)$. Compared with the results of $(\rho_A^i,\phi_A^i)$, the errors on parameter $(\rho_A^f, \phi_A^f)$ are relatively small (see Table \[pikfit\]), because the available measurements on branching ratios for $B$ ${\to}$ ${\pi}K$ decays are highly precise. The conjecture about $(\rho_A^f, \phi_A^f)$ in [@zhu2] is somewhat alike to our fit results of Part A.

The value of term $(2X_A^f-X_A^f)$ in Eq.(\[af3\]) is about $(27.2-i26.2)$ with parameters for Part A and $(28.9-i25.5)$ for 