in SM. It is argued [@Cheng1; @pipipuz] that to solve the so-called ${\pi}K$ puzzle, a large complex color-suppressed tree amplitude $C^{\prime}$ or a large complex electroweak penguin contribution $P_{\rm EW}^{\prime}$ or a combination of them are essential. An enhanced complex $P_{\rm EW}^{\prime}$ with a nontrivial strong phase can be obtained from new physics effects [@pipipuz]. To get a large complex $C^{\prime}$, one can resort to spectator scattering and final state interactions [@Cheng1; @Cheng2]. Recently, the annihilation amplitudes with large parameters $\rho_A$ is suggested to conciliate the recent measurements Eq.(\[HFAGpipi\]) and Eq.(\[HFAGKK\]), so surprisingly, the ${\pi}K$ puzzle is also resolved simultaneously [@zhu2]. Theoretically, the power corrections, such as spectator scattering at the twist-3 order and annihilation amplitudes, are important to account for the large branching ratios and $CP$ asymmetries of penguin-dominated and/or color-suppressed tree-dominated $B$ decays. So, before claiming a new physics signal, it is essential to examine whether power corrections could retrieve “problematic” deviations from the SM expectations. Interestingly, our study show that with appropriate parameters, the annihilation and spectator scattering contributions could provide some possible solutions to the $\pi K$ and $\pi \pi$ puzzles.

Our paper is organized as following. In section \[sec02\], we give a brief overview of 