Why did north and South Korea split?

When the japan surrended in 1945 in second world war, USA and USSR rushed to korea and ussr took the north part of Korea and USA took the south part because korea was colony of japan. That time there was korean government and they asked usa and russia to go away from country but the usa government ignored it. And made army government by force. Eventhough many korean people argue against and ask them to leave, us and ussr government divided the country into half by their advantage. But because of this many korean people suffer. So the north and south korea was formed.