The pudding empire's home planet only has a lifespan left of one year. Thus, they aim to invade Earth and make it their own... but first they've got to wipe out those annoying humans who are currently inhabiting the planet. Planning an invasion turns out to be much easier said than done, especially when your human-killing monsters start having problems with morale, sickness, family issues, and so forth...

From Rayns&Lele Scans:

No matter how you look at it, Kamijou is an average guy. On the other hand, his ex-childhood friend, Aikawa Itasu, is a popular and intelligent girl. Believing his childhood friend to be in a whole other world than himself, he starts putting distance between them...
Until one day, Kamijou’s cat, Peace, sneaks off and visits Aikawa. The two of them starts talking again. What's Aikawa's motive for feeding Peace? And... will they end up reconnecting?