What happens in the end of Fruits basket for yuki?

Yuki ends up with Machi. Machi Kuragi is a girl off the student council.

Yuki's curse broke last. He was with Machi when the curse broke, and he felt it break, and he then hugged her, and then kissed her. Normally she calls him Class President, but then he tells her to call him by first name, Yuki (he kissed her when she said his name a couple times)

Later, after graduating, he will be going to college, so he got a new apartment. He gives Machi his apartment key and tells her to come by any time.

In the end, they will be together and get married in the future and have a daughter, I read online but it doesn't really say, but apparently the little girl in the end wasn't ONLY Kyo and Tohru's granddaughter, but also Yuki and Machi's