A solution contains some or all of the ions Cu^{2+}, Al^{3+}, K^+, Ca^{2+}, Ba^{2+}, Pb^{2+}, and {NH_4}^+. The following tests were performed, in order, on the solution. 1.Addition of 6 M M HCl \rm HCl produced no reaction. 2.Addition of H 2 S \rm H_2S with 0.2 M M HCl \rm HCl produced a black solid. 3.Addition of (NH 4 ) 2 S \rm (NH_4)_2S produced a white solid. 4.Addition of (NH 4 ) 2 HPO 4 \rm (NH_4)_2HPO_4 in NH 3 \rm NH_3 produced no reaction. 5.The final supernatant when heated produced a purple flame. Identify which of these ions were present in the solution, which were absent, and for which ones no conclusions can be drawn.