US President George W. Bush and Prime Minister Ehud Olmert bid each other farewell on Monday, expressing confidence in an eventual Middle East peace deal that won't materialize on either of their watches. Bush and Olmert met at the White House as their time in office winds to a close. Bush's second term ends Jan. 20, while Olmert plans to resign amid corruption charges and will step down after a successor is chosen on Feb. 10. Speaking to reporters before their talks in the Oval Office and a private dinner with the two men's families, Bush said the two leaders have been through a lot together. Olmert said history will owe Bush a debt of gratitude for setting the region on the path to an accord. "The two-state solution is the only possible way to resolve the problem in the Middle East," Olmert said.