chess puzzle

This puzzle is interesting; after c7 Black can play Rd6+.
Now If the king goes to c6, then Rd1! gives Black a draw after c8=Q Rc1+ Kb7 and Rxc8.
If the king goes to b7, then Rd7! and the pawn will be swapped off for the rook, also a draw.
Even Kb5 draws, as now Black will now keep checking White until he goes onto the c-file or seventh rank.
This position is a draw.
EDIT: See my next post, this analysis is wrong.

This puzzle is interesting; after c7 Black can play Rd6+.
Now If the king goes to c6, then Rd1! gives Black a draw after c8=Q Rc1+ Kb7 and Rxc8.
If the king goes to b7, then Rd7! and the pawn will be swapped off for the rook, also a draw.
Even Kb5 draws, as now Black will now keep checking White until he goes onto the c-file or seventh rank.
This position is a draw.
You're wrong. The position is winning for White.
Sorry, I noticed as I posted that White can win by Kb5!.
After Rd5+, White can move his King down the b-file as Black checks and bring it to b3. When Black plays Rd3+, white plays Kc2 and there is no Rd1.
I'll post a diagram