$24^{+2+5}_{-2-4}$              $10.3$
  $\bar{B}^0 \to \pi^0 \pi^0$         $43 \pm 24$            $46^{+3+6}_{+3-6}$                  $38^{+2+6}_{-2-6}$              $-19.0$

  : The direct CP asymmetries (in units of $10^{-2}$) of $B$ ${\to}$ $\pi K$, $K \bar{K}$, $\pi \pi$ decays. The notes on uncertainties are the same as Table\[pikbr\].[]{data-label="pikdcp"}

                                     Exp. [@HFAG]         scenario I              scenario II       
  --------------------------------- --------------- ----------------------- ----------------------- --
  $\bar{B}^0 \to \pi^0 \bar{K}^0$     $57 \pm 17$     $78^{+3+1}_{-3-1}$      $79^{+3+1}_{-3-1}$    
  $\bar{B}^0 \to K^- K^+$                  —          $-86^{+6+0}_{-5-0}$     $-86^{+6+0}_{-5-0}$   
  $\bar{B}^0 \to K^0 \bar{K}^0$      $-108 \pm 49$    $-10^{+1+0}_{-1-0}$     $-11^{+1+0}_{-1-0}$   
  $\bar{B}^0 \to \pi^+ \pi^-$         $-65 \pm 6$    $-59^{+11+2}_{-10-3}$   $-60^{+10+2}_{-10-2}$  
  $\bar{B}^0 \to \pi^0 \pi^0$              —          $77^{+6+1}_{-8-2}$      $77^{+7+1}_{-9-2}$    

  : The mixing-induced $CP$ asymmetries (in units of $10^{-2}$) of $B$ ${\to}$ $\pi K$, $K \bar{K}$, $\pi \pi$ decays. The notes on uncertainties are the same as Table\[pikbr\].[]{data-label="pikmcp"}

To get more information on annihilation and spectator scattering, we perform a fit on the parameters $X_H$ $=$ $X_A^i$ and $X_A^f$, considering the constraints of the $CP$-averaged branching ratios, direct and mixing-induced $CP$-asymmetries, from $B$ ${\to}$ $\pi K$, $K \bar{K}$ decays. The experimental data are summarized in the second column of Tables \[pikbr\]-\[pikmcp\]. Our fitting results are shown by Fig.\[ParaSpacI\], and the corresponding numerical results are listed in Table \[pikfit\]-\[pikmcp\].

It is found that two possible solutions entitled Part A 