Black must clearly promote a pawn or two in order to suffocate his king with his own men. The simplest idea would be to have the king on h6, hemmed in by bishops on g6 and h5 to allow Bc1 mate, but it cannot be done: while the g-pawn can reach f1 or h1, the a-pawns can only promote on a1, which is a black square.
No, it's going to take more than two promotions, and that means the bishop on a3 will have to be captured. Having reached that conclusion, we can now guess the final position: with black men on e4, e5, f5, g5 and g3, White will play hxg3 mate. Black needs 18 moves to promote all five a-pawns, which leaves only two moves for each promoted man to reach its destination.
Since a queen on a1 would deliver check, it has to be done with rooks. Here goes: 1.a1=R, 2.Rxa3, 3.Rg3, then a3, a2 and 6.a1=R, 7.Ra4, 8.Re4, 12.a1=R, 13.Ra5, 14.Rg5, 19.a1=R, 20.Raa5, 21.Raf5, 26.a1=R, 27.Raa5, 28.Raf5 and White plays hxg3 mate. Bravo!Reuse content