This is based on these pictures (Art not mine, all art belongs to the original artist!!) 

Now for the story! 

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Kay had returned to the dorms, having what she thought was a regular, fluffy, dog, whose fur was ashy blonde. Despite his aggressive demeanor, he was quite sweet to the girl. "Hey guys! I got a pet!" she said as she walked into the dorms, everyone looking at the big dog. "...Did you get it from the woods?" Koy asked, the 'dog' growled slightly, but Kay petted his head to calm him. "No, I found him wandering on the side of the road, he was hurt and I helped him, he was a little hesitant at first, but warmed up to me," she said, smiling at the dog. "Aw, he's so fluffy!" Denki said, going to pet him, but the dog growled at him. "He's...not friendly..." 

"Yeah, he seems to really only trust me, but I'm sure he'll warm up to everyone." 

"Hopefully he won't try to eat Koda's bunny..." 

"W-what...he won't...r-right...?" 

"No! I won't let him go to your room, I'll keep him in my room and the common room, and outside when he needs to use the bathroom." 

Kay walked the dog to her dorm room, the dog keeping close to her while eyeing the other people. Kirishima looked at Koy. "Do you think it's safe...?" he asked, Koy shrugged. "If he didn't bite her face off, then I guess, most animals do like Kay, so I'm sure it'll be fine." 

Later that night, Kay was studying in the common area with some of her classmates, when her dog came up and layed on her lap, despite being really big. "Hehe, he really likes you," Mina said with a smile. "Yeah, he's really clingy," Kay said with a giggle, petting him. "Have you come up with a name?" Ochaco asked, smiling softly. "Yeah, I decided to go with Katsuki." 

"That's a great name!" 

"Thanks, hehe!" 

Kay studied for a while before Katsuki moved his head to her lap, laying on her notes. "Hehe, someone wants to cuddle," she said, hugging the fluffy dog. After a while, everyone else went and did their own thing, while Kay layed there with her dog. She was pretty relaxed and soon fell asleep hugging him. Katsuki looked around, seeing they were alone, and the dog...rather, wolf, changed his form into a human, having wolf ears and a tail, but kept hugging her. "Thank you for saving me..." he whispered, closing his eyes as he cuddled her. 

Soon, however, Denki was walking by to get a drink, but then saw Katsuki in his human form, laying on Kay. It didn't register at first, but he looked back, Katsuki staring at him, and quickly went back into his wolf form, letting out a slight growl at Denki. "W-what the...?" Denki quickly grabbed his drink and went back to his room. 

The next day

Kay had gone out with some friends, so only a couple of people were there. Denki was still freaking out. 

"Hey." 

Denki turned, seeing Katsuki on the couch in his human form, grinning at him. 

"Bitch." 

Denki then called out for Iida. 

"Iida! Come and look!" He yelled, but as soon as Iida entered, Katsuki went back to his wolf form, grinning at Denki. "What is it?" Iida asked curiously, Denki stood there, dumbfounded. "I...I..."  

"Is something wrong?" 

"N...no..." 

Iida shrugged, leaving the room. Once he was gone, Bakugou went back to his human form. "Look...no one is going to know about this, got it? Not even Kay, she saved me, and I quite like her...so you rat me out, I'm going to chew on your bones, got it?" he asked, Denki gulped and nodded. "G-got it..." Katsuki chuckled, before going into his wolf form, laying his head down and napping. 

"We're living with a werewolf...this is crazy..." Denki said, walking off.