Hanbun no Tsuki ga Noboru Sora Looking Up At The Half-Moon
During the winter, Yuichi was hospitalized due to hepatitis. Randomly he would try to escape from the hospital but would get beat up by the nurse. One day, he happened to meet Rika, a girl of his age, in the next building. He was fascinated by her beauty, but she was very selfish girl. Although she led him by the nose, he began to be attracted by her. However, when Rika told him about her illness, he knew why she acted so selfish; she didn't have long to live.
[Source: Anime News Network]