A Zinar Puzzle From The Moscow Tournament

Another study from the great Zinar. How can white escape with a draw here?

6K1/k7/p1P5/1P6/7p/8/PP6/8 w - - 0 1

1.Kf7 Kb6
2.Ke6 Kc7
3.Kd5 h3
4.b6+ Kxb6
5.Kd6 h2
6.c7 h1=Q
7.c8=Q Qh2+
8.Kd7 Qd2+
9.Ke6 Qe3+
10.Kd7 Qd2+
11.Ke6 Qe3+
12.Kd7 Qd2+
It's a draw.

It's an interesting variation too. At first I couldn't find the fifth move.
1.Kf7 Kb6
2.Ke6 Kc7
3.Kd5 axb5
4.Ke4 Kxc6
5.a3 h3
6.Kf3 h2
7.Kg2 Kd5
8.b3 h1-Q
9.Kxh1 Kd4
10.a4 bxa4

In the interesting variation, Alena, the 5th move isn't the only draw for white. He can move the king to the king side to win the h-pawn while leaving both pawns, for the moment, on a2 and b2 while the black king advances through d3 and c2 to attack them. However, once attacked, white must then find two only moves to draw. Can you find that line?

Here is the position I am talking about: 8/8/8/1p6/8/6K1/PPk5/8 w - - 0 1


1.b4 Kc3
2.Kf4 Kxb4
3.Ke5 Kc5
4.Ke4 b4
5.Ke5 b3


1.b4 Kb2
2.a4 bxa4
3.b5 a3
4.b6 a2
5.b7 a1=Q