Question: In what county would you find Carpenter which shares a state with Cold Brook Dam?

full_context: Document 1: Carpenter, Oklahoma: Carpenter is an unincorporated community in Roger Mills and Custer counties in the state of Oklahoma, United States. The community is eight miles north of Elk City, Oklahoma.
Document 2: Renner, South Dakota: Renner is an unincorporated community in Minnehaha County in the U.S. state of South Dakota. Renner has been assigned the ZIP code of 57055. The demographics of Renner are not listed separately by the United States Census Bureau, but are included within those of Mapleton Township. The 2000 Census reported a total population of 2,128 for all of Mapleton Township.
Document 3: Sweetwater Dam: The Sweetwater Dam is a dam across the Sweetwater River in San Diego County, California. It is located approximately east of San Diego, and borders Bonita to the southwest and La Presa to the northeast. The -high masonry arch dam impounds Sweetwater Reservoir.
Document 4: Rapid Creek (South Dakota): It rises in southwestern South Dakota, in the Black Hills National Forest in the Black Hills in Pennington County. It flows east, is joined by Castle Creek, past Silver City and through the Pactola Reservoir. Emerging from the Black Hills, it flows through Rapid City, past Farmingdale, and joins the Cheyenne River approximately 13 mi (21 km) southwest of Wasta.
Document 5: Cold Brook Dam: Cold Brook Dam is a dam in Fall River County, South Dakota in the southwestern part of the state, south of the Black Hills.
Document 6: Keyhole State Park: The Keyhole Reservoir, an impoundment of the Belle Fourche River, was formed by the Keyhole Dam project of the United States Bureau of Reclamation, completed in 1952. The reservoir has a total capacity of 334,200 acre-feet and water surface of 13,700 acres, which provides storage for irrigation, flood control, fish and wildlife conservation, recreation, sediment control, and municipal and industrial water supply. Although located in Wyoming, the reservoir's waters are allocated by compact to go 90 percent to South Dakota and 10 percent to Wyoming.
Document 7: Carpenter, Iowa: As of the census of 2010, there were 109 people, 47 households, and 27 families residing in the city. The population density was 681.3 inhabitants per square mile (263.1/km2). There were 51 housing units at an average density of 318.8 per square mile (123.1/km2). The racial makeup of the city was 98.2% White and 1.8% African American.
Document 8: Deerfield Dam: Deerfield Dam is a dam impounding Castle Creek in the Black Hills of South Dakota. The dam creates Deerfield Reservoir within the Black Hills National Forest.
Document 9: Watauga, South Dakota: Watauga is an unincorporated community in Corson County, South Dakota, United States. Although not tracked by the Census Bureau, Watauga has been assigned the ZIP code of 57660.
Document 10: Andrew Carpenter House: The Andrew Carpenter House on State Road 1820 in Gaston County, North Carolina, is believed to have been built for Andrew Carpenter shortly after his marriage to Sophia Smith on April 19, 1831. The two-story Federal style plantation house is two rooms deep and has paired chimneys. It is one of the largest early-19th century houses in Gaston County.
Document 11: Bath, South Dakota: Bath is an unincorporated community and census-designated place in Brown County, South Dakota, United States. As of the 2010 census, Bath had a population of 172. Bath has been assigned the ZIP code of 57427.
Document 12: Carpenter, South Dakota: Carpenter is an unincorporated community in Clark County, South Dakota, United States. Although not tracked by the Census Bureau, Carpenter has been assigned the ZIP code of 57322.
Document 13: Belle Fourche Dam: The Belle Fourche Dam, also known as Orman Dam, is a dam on Owl Creek in Butte County, South Dakota, USA, approximately eight miles east of Belle Fourche, South Dakota, along U.S. Route 212. Its construction created the Belle Fourche Reservoir, the Belle Fourche National Wildlife Refuge, and the Rocky Point Recreation Area.
Document 14: South Fork Grand River (South Dakota): It rises in the Badlands of northwestern South Dakota, south of the Cave Hills in western Harding County, and flows east past Buffalo, then past several units of the Grand River National Grassland in northern Perkins County. It joins the North Fork in the Shadehill Reservoir near to form the Grand, which is a tributary of the Missouri.
Document 15: Canton, South Dakota: Canton is a city in and the county seat of Lincoln County, South Dakota, United States. Canton is located 20 minutes south of Sioux Falls in southeastern South Dakota. Canton is nestled in the rolling hills of the Sioux Valley, providing an abundance of recreational activities with the Big Sioux River bordering the eastern side, Newton Hills State Park to the south, and Lake Alvin to the north. The city was named by Norwegian settler and former legislator James M. Wahl. The population is estimated to be 3,430 as of 2017.
ground_truth: Clark County
sub_queries: Which state is Cold Brook Dam located? Answer: South Dakota
Carpenter, South Dakota >> located in the administrative territorial entity Answer: Clark County