A 0.649 g sample containing only K2SO4 (174.27 g/mol) and (NH4)2SO4 (132.14 g/mol) was dissolved in water and treated with Ba(NO3)2 to precipitate all sulfate as BaSO4 (233.39 g/mol). If 0.977 g of precipitate was formed, what is the mass percent K2SO4 in the sample?