Question: The Bozeman Trail was a direct route to the Montana gold fields through an area loosely defined as that between the Bighorn Mountains what hills?

Context paragraphs:
Smoky Hill Trail: The Smoky Hill Trail was an American trail across the central Great Plains of North America in use from 1855 to 1870.  Established in what was then Kansas Territory, it extended west from Atchison, Kansas on the Missouri River to Denver, spanning the length of what is today Kansas and the eastern portion of Colorado.  The trail was named after the Smoky Hill River whose course it paralleled for much of its length.  Used by prospectors as the most direct route west to the Colorado gold fields during the Pike's Peak Gold Rush, it later served as a path westward for American settlers before being gradually superseded by the Kansas Pacific Railway.

John Bozeman: John Merin Bozeman (January 1837 – April 20, 1867) was a pioneer and frontiersman in the American West who helped establish the Bozeman Trail through Wyoming Territory into the gold fields of southwestern Montana Territory in the early 1860s.  He helped found the city of Bozeman, Montana in 1864, which is named for him.

Cloud Peak Wilderness: The Cloud Peak Wilderness is located in north central Wyoming in the United States.  Entirely within Bighorn National Forest, the wilderness was established in 1984 in an effort to preserve the wildest section of the Bighorn Mountains.  The wilderness has the highest peaks in the Bighorn Mountains including Cloud Peak and Black Tooth Mountain, as well as Cloud Peak Glacier, the only remaining active glacier in the Bighorn Mountains.  The Cloud Peak Wilderness is 189039 acre .

Yarra Track: The Yarra Track is the former name of the gold fields road from Healesville to the Woods Point and Jordan Goldfields, in Victoria, Australia.  A direct route via the Yarra River and the Great Divide, was discovered by Reick in September 1862.  This became known as the `Yarra Track’.  Early in 1863, the Government decided to construct a road along the route.  Its original width varied between 12 and 20 feet, and was designed to accommodate horse-drawn vehicles.  This Track involved the climbing of the Black Spur, descent into the Acheron Valley, and then through Marysville to the Cumberland where it followed the existing route.  The old route through Paradise Plains subsequently dropped out of vogue.

Bridger Trail: The Bridger Trail, also known as the Bridger Road and Bridger Immigrant Road, was an overland route connecting the Oregon Trail to the gold fields of Montana.  Gold was discovered in Virginia City, Montana in 1863, prompting settlers and prospectors to find a trail to travel from central Wyoming to Montana.  In 1863, John Bozeman and John Jacobs scouted the Bozeman Trail, which was a direct route to the Montana gold fields through the Powder River Country.  At the time the region was controlled by the Sioux, Cheyenne and Arapaho, who stepped up their raids in response to the stream of settlers along the trail.

Powder River Country: The Powder River Country is the Powder River Basin area of the Great Plains in northeastern Wyoming, United States.  The area is loosely defined as that between the Bighorn Mountains and the Black Hills, in the upper drainage areas of the Powder, Tongue, and Little Bighorn rivers.

Cloud Peak Glacier: Cloud Peak Glacier is in the Bighorn Mountains in the northcentral section of the U.S. state of Wyoming.  Centered within the Cloud Peak Wilderness of Bighorn National Forest, Cloud Peak Glacier is the only active glacier in the Bighorn Mountains.  The glacier is in a deep cirque immediately northeast of Cloud Peak, the highest peak in the Bighorn Mountains.  Cloud Peak Glacier lies at approximately 11800 ft above sea level.

Bozeman Trail: The Bozeman Trail was an overland route connecting the gold rush territory of Montana to the Oregon Trail.  Its most important period was from 1863–68.  Despite its name, "the major part of the route in Wyoming used by all Bozeman Trail travelers in 1864 was pioneered by Allen Hurlbut".  Many miles of the Bozeman Trail in present Montana followed the tracks of Bridger Trail, opened by Jim Bridger in 1864.  The flow of pioneers and settlers through territory of American Indians provoked their resentment and caused attacks.  The challengers to the route were newly arrived Lakotas and their Indian allies, the Arapahoe and the Cheyenne.  The United States put emphasis on a right to "establish roads, military and other posts" as described in Article 2 in the Fort Laramie Treaty of 1851.  All parties in the conflict had signed that treaty.  The Crow Indians held the treaty right to the contested area and had called it their homeland for decades.  They sided with the whites.  The U.S. Army undertook several military campaigns against the hostile Indians to try to control the trail.  Because of its association with frontier history and conflict with American Indians, various segments of the trail are listed on the National Register of Historic Places (NRHP).

Nelson Story: Nelson Story, Sr. (April 4, 1838 – March 10, 1926) was a pioneer Montana entrepreneur, cattle rancher, miner and vigilante, who was a notable resident of Bozeman, Montana.  He was best known for his 1866 cattle drive from Texas with approximately 1000 head of Texas Longhorns to Montana along the Bozeman Trail—the first major cattle drive from Texas into Montana.  His business ventures in Bozeman were so successful that he became the town's first millionaire.  In 1893, he played a prominent role in the establishment of the Agricultural College of the State of Montana by donating land and facilities.  He built the first "Story Mansion" on Main Street in Bozeman in 1880 and later built today's Story Mansion at the corner of Willson and College for his son, T. Byron Story in 1910.  In his later years, he became a prominent real estate developer in Los Angeles, California.

K. S. Vasan: K.S. Vasan was an Indian communist politician and trade unionist from the Kolar Gold Fields.  who organized the first leftist trade union in the gold fields during the 1940s.  Vasan, then a young man, arrived at the Kolar Gold Fields from Madras and went on to build a union that mobilized labourers from thirteen different mining companies.  He was arrested as he led a workers revolt against the British authorities.

Supporting paragraphs: Bridger Trail Powder River Country
Answer: Black Hills