60...Ka1 61.Kf6 d4 62.g7 Qc6+ 63.Kg5 Qd5+ 64.Qf5 Qg2+ 65.Kf6 Qc6+ 66.Qe6 Qf3+ 67.Ke7 Qb7+ 68.Qd7 Qe4+ 69.Kd6 Qf4+ 70.Kc5 Qc1+ 71.Kb6 Qb1+ 72.Kc7 Qc1+ 73.Qc6 Qf4+ 74.Kb6 Qb8+ 75.Ka6 Qg8 76.Qa4+ Kb1 77.Qxd4 Qa8+ 78.Kb5 Qb7+ 79.Kc4 Qc6+ 80.Qc5 Qe6+ 81.Kb4 Qg4+ 82.Kb3 Qe6+ 83.Ka4 Qa2+ 84.Qa3 Qg2 85.Qb4+ Ka1 86.Qa5 Kb1 87.Qb5+ Ka1 88.Qe5+ Kb1 89.Qb8+ Ka1 90.g8=R (90.g8=Q? Qe4+ 91.Kb5 Qc6+ =) Qa2+ 91.Kb4 Qa3+ 92.Kc4 Qc1+ 93.Kd4 Qd1+ 94.Ke4 Qe1+ 95.Kf4 Qf1+ 96.Kg4 Qg2+ 97.Qg3 Qe4+ 98.Kh3 Qh1+ 99.Qh2 Qf3+ 100.Rg3 Qf5+ 101.Kg2 Qd5+ 102.Rf3 Qe4 103.Qg1+ Kb2 104.Qe3 Qd5 105.Kf2 Kb1 106.Qd3+ Qxd3 107.Rxd3 Kb2 108.Ke1 Kc2 109.Ke2 Kb1 110.Kd2 Kb2 111.Rf3 Kb1 112.Kc3 Ka2 113.Rf1 Ka3 114.Ra1 mate.
The following line is not more efficient than the one above, but employs a "straighter path" (i.e. fewer branches).
77.Qxd4 and now 77...Qc8+ 78.Kb5 Qb7+ 79.Kc4 Qc6+ 80.Qc5 Qe6+ 81.Qd5 Qg4+ 82.Qd4 Qc8+ 83.Kb3 Qc2+ 84.Kb4 Qg2 85.Kc5 Qg5+ 86.Kb6 Qg6+ 87.Ka5 Qg5+ 88.Ka6 Qg3 89.Qd1+ Kb2 90.Qe2+ Ka1 91.Qf1+ Kb2 92.Qf7 Qd3+ 93.Ka7 Qa3+ 94.Kb7 Qb4+ 95.Ka8 Qa5+ 96.Qa7 Qg5 97.Qb7+ Ka1 98.Qf7 Qg2+ 99.Ka7 Qg1+ 100.Ka6 Qg2 101.g8=Q Qc6+ 102.Ka7 Qa4+ 103.Kb8 Qb5+ 104.Ka8 Qc6+ 105.Qb7 Qa4+ 106.Qa7 and mate on move 114.