A missing Washington state family was found safe Thursday after hunters spotted them walking along a remote logging road two days after they failed to pick up their older kids from school, authorities said.

Jason and Melissa McAlister were out for a drive Tuesday with their 8-month-old and 2-year-old, and got stuck when the road gave way as they tried to maneuver their van around a downed tree in Mason County.

"Everybody's good. God's great. Happy to be alive," 33-year-old Jason McAlister told reporters.

"This one was a trouper," he said, referring to his 2-year-old daughter. "She was rooting around in the van, finding all kinds of Halloween candy."

The family began to trek back toward the main road at about 1 p.m. Tuesday, but stopped as darkness began to set in, he said. He made shelter along the side of the road by leaning fir boughs against a rock face that protected them from the wind as temperatures plummeted into the 30s.

"It actually kept us warm, considering I didn't have a fire going," he said.

McAlister usually keeps lighters in the car as a safety precaution – he doesn’t smoke. But the friends that do smoke had borrowed them at the time.

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The family turned around and headed back to the van Wednesday to try to get warm and dry their clothes. They spent the night in the van and learned that authorities had been looking for them. On Thursday morning, the parents, using a spiral notebook the older kids, ages 5 and 7, had left in the van, began tearing sheets from it and leaving them on the ground in wide spots of the road where they might be seen by helicopter crews.

That's when the hunters found them, Jason McAlister said. McAlister formerly served as a volunteer firefighter for Cowlitz County, where he also worked search-and-rescue, and he said he was grateful for the efforts of everyone who had been looking for his family.

The hunters immediately recognized them because of heavy media coverage about the search, said Steve Shumate, chief criminal sheriff's deputy in neighboring Grays Harbor County, where the family lives. They called 911, drove the family to a general store to meet medics and then led deputies to the family's van.

It was an immense relief for authorities, who feared a less happy ending when the family failed to turn up Wednesday.

"We figured if they were going to walk out, that's when it would have happened," Shumate said.

The family's home is in a rural area southwest of Seattle, about 20 miles north of the town of Montesano. They were reported missing Tuesday evening after no one showed up to meet the school bus bringing the older children home, Shumate said. Jason McAlister works as a ranch hand on the property, and Melissa McAlister works at a Walmart store.

"Hopefully they'll learn some lessons about having a working cellphone with them and letting people know where they're going," Shumate said. "But they did an excellent job keeping their cool and staying dry and warm."

McAlister said he probably won't get a cellphone, because there's no service where the family lives. But he said he learned one lesson.

He added that he believes his volunteer firefighter training helped him keep calm during the 48 hours in the rugged terrain, according to Q13 Fox.

Next time, he said, he'll "take the truck instead of the family church rig."

The Associated Press contributed to this report.

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