SEATTLE -- The two mountain bikers did what they were supposed to do when they noticed a mountain lion tailing them on a trail east of Seattle: They got off their bikes.

They faced the beast, shouted and tried to spook it. After it charged, one even smacked the cougar with his bike, and it ran off.

It wasn't enough, authorities said.

As they stood trying to catch their breath, the cougar returned, biting one of them on the head and shaking him, Capt. Alan Myers of the Washington Department of Fish and Wildlife Police said Sunday.

"He said he had his whole entire head in the jaws of this animal and was being shaken around horribly," Myers said.

The second cyclist ran, and the animal dropped the first victim and pounced on him, killing him and dragging him back to what appeared to be its den.

"They did everything they were supposed to do," King County sheriff's Sgt. Ryan Abbott said. "But something was wrong with this cougar."

The attack Saturday near North Bend, in the Cascade Mountain foothills 30 miles east of Seattle, was the first fatal cougar attack in the state in 94 years. Myers said Sunday that the cougar was underweight - about 100 pounds, when a typical 3-year-old male in the area would be 140 to 180 pounds.

Officials said there was no indication that the victims taunted the big cat, CBS News correspondent DeMarco Morgan reports.

The 31-year-old Seattle man who was bitten first, Isaac Sederbaum, survived. Rescuers flew him to a hospital, where he was in satisfactory condition Sunday, Harborview Medical Center spokeswoman Susan Gregg said.

Myers identified the deceased victim, a 32-year-old Seattle resident, as S.J. Brooks.

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