MEDICINE LODGE, Kan. - Winds that have hindered firefighters trying to contain the biggest wildfire in Kansas history are forecast to increase.

The National Weather Service says a strong southeast wind of 20 to 30 mph is expected to blow over the sparsely populated fire zone Monday and Tuesday. Gusts of around 40 mph are forecast both days.

Regardless, officials report the Anderson Creek fire is 80 percent contained, according to CBS affiliate KWCH in Kansas.

Get Breaking News Delivered to Your Inbox

In Kansas, almost 400,000 acres has burned, according to officials. The blaze has consumed at least 620 square miles since it started last week in Oklahoma and spread across the border.

While the winds could spread embers, an increase in humidity Tuesday could help firefighters. Up to 4 inches of snow that fell over the area Sunday could also assist in efforts to contain the blaze.

The Kansas Adjutant General's Office says six homes have been destroyed and some livestock lost. No people have been seriously injured.

So far, the cost in combating the Anderson Creek fire has reached more than $1 million, not including costs for Barber County crews, reports KWCH.