(Adds quotes, details, updates prices) By Karen Brettell NEW YORK, April 13 (Reuters) – The dollar fell to a two-month low against a basket of currencies and a one-year low against the euro on Thursday after U.S. producer prices unexpectedly fell in March, boosting expectations that the Federal Reserve is near the end of its rate hiking cycle. The producer price index (PPI) for final demand dropped 0.5% last month. In the 12 months through March, the PPI increased 2.7%. That was the smallest year-on-year rise since January 2021 and followed a 4.9% advance in February. It comes after consumer price index (CPI) inflation data on Wednesday came in at 5% year-on-year in March, down from 6% in February. Core inflation – which strips out volatile food and energy prices – picked up to 5.6%, from 5.5% the previous month. “We are headed back to a low inflation world, that’s the message of the market right…