We have one legal kick and one illegal kick. The second kick is illegal since it occurred after a change of possession. So we've got a foul for illegal kicking at the 35. For purposes of spots, illegal kicks are treated as fumbles, so it's as if a fumble went out of bounds at the 50. Under all-but-one, I'd enforce the illegal kicking penalty (15 yards) from the 35. But, since K was in possession of the ball after a legal kick, I'd still give them the ball.
1st and 10 for Team K at the 20?