of Fig. \[fig:size\], we show that at $t=3$ Gyr, the evolutionary trend seen at $t=1$ Gyr is more pronounced. Coagulation further proceeds especially in the dense medium, producing a smooth power-law-like grain size distribution similar to the MRN grain size distribution \[$n(a)\propto a^{-3.5}$\]. The effect of dust growth by accretion is also imprinted in the grain size distribution in the diffuse ISM as seen in the bump around $a\sim 0.01~\micron$. This imprinted bump is caused when these particles were previously included in the dense ISM, [where accretion could take place efficiently if the metallicity is high enough.]{} Because of the variety in the past history, the diffuse gas particles have larger variation in the grain size distribution especially at small grain radii than the dense ones. In some regions as shown in the lower 25th percentile, there is no bump at small grain radii, indicating that accretion has not yet been efficient. Thus, we predict that there is a large variety in the dust abundance in the diffuse ISM.

![Evolution of grain size distribution for the entire galactic disc at $t=0.3$, 1, and 3 Gyr from top to bottom. The blue and red lines show the median grain size distribution 