WASHINGTON, March 9 (Reuters) - The U.S. Treasury will work to quickly distribute $350 billion in aid to state and local governments from President Joe Biden’s coronavirus stimulus bill, Treasury Secretary Janet Yellen said on Tuesday, adding that it should bring “some measure of prosperity” after the pandemic ends. “In the coming days our Treasury team is going to work to get this aid out in the quickest way possible, and the one that produces the greatest economic impact,” Yellen said in remarks to a National League of Cities conference. (Reporting by David Lawder; Editing by Leslie Adler)