Question: which town in Rensselaer County, New York, United States did  Valley Falls, New York village lies on the boundary

<P0-S0>  The population was 7,679 at the 2010 census. <P0-S1>  It was named for the Schaghticoke, a Native American tribe formed in the seventeenth century from an amalgamation of remnant peoples of eastern New York and New England. <P0-S2>  The tribe has one of the oldest reservations in the United States, located in what is now Litchfield County, Connecticut. <P0-S3>  It has been recognized by the state of Connecticut but has not yet achieved federal recognition. <P0-S4> Schaghticoke is a town in Rensselaer County, New York, United States. <SEP> <P1-S0>  The village lies on the boundary of the towns of Pittstown and Schaghticoke, but is mostly in the northwest part of Pittstown. <P1-S1> Valley Falls is a village in Rensselaer County, New York, United States. <P1-S2>  The population was 466 at the 2010 census. <SEP> <P2-S0> Seneca Falls is a hamlet (and census-designated place) in Seneca County, New York, in the United States. <P2-S1>  The population was 6,681 at the 2010 census. <P2-S2>  The hamlet is in the Town of Seneca Falls, east of Geneva. <P2-S3>  It was an incorporated village from 1831 to 2011. <P2-S4>  Seneca Falls became the largest New York village ever to approve dissolution after village residents voted to dissolve it in 2010. <SEP> <P3-S0> <br><br>The New York, Susquehanna and Western, formerly the Midland Railroad, the Jersey City and Albany Railroad, and the Northern Railway of New Jersey—all running northward through the township— afford ample railroad accommodations. <P3-S1>  Sloops and schooners can pass up this creek nearly to the northern boundary of the township. <P3-S2>  Bellman's Creek, forming part of the southern boundary, the Hackensack, the Overpeck, the Hudson, with more than a dozen other smaller streams and rivulets, bountifully supply the whole township with water. <P3-S3>  Much of the area had been during the colonial area known as the English Neighborhood. <P3-S4> Ridgefield Township was a township that existed in Bergen County, New Jersey. <P3-S5>  It has, however, an independent line projected and now under construction to New York City. <P3-S6>  From the western border of the Palisades the land descends to the Overpeck, forming a most beautiful valley, with the land again rising to a high ridge midway between the Overpeck and the Hackensack. <P3-S7>  The Westervelts, the Zimcrmans, the Bantas, and the Blauvelts, all coming from Holland, settled in the middle of the seventeenth century in that locality. <P3-S8>  His first impressions are much like those of old Hendrick Hudson in speaking of a wider extent of country: "A very good land to fall in with, and a pleasant land to see." <P3-S9>  The township was created in 1871, when Hackensack Township was trisected to form Palisades Township in the northernmost third, Englewood Township in the central strip and Ridgefield Township encompassing the southernmost portion, stretching from the Hudson River on the east to the Hackensack River, with Hudson County to the south. <P3-S10>  From this long ridge, extending far to the north beyond this township, it took its name of Ridgefield. <P3-S11>  Ridgefield embraces the earliest settlements in the ancient township of Hackensack, antedating even the organization of that township in 1693, and of the county of Bergen in 1675. <P3-S12>  The Susquehanna enters the township at Bellman's Creek, and the Northern at about one hundred feet south of the creek, and at a point north and east of the Susquehanna. <P3-S13>  As described in the 1882 book, "History of Bergen and Passaic counties, New Jersey," "Ridgefield is the first township in Bergen County which the traveler enters in passing up the Palisades. <P3-S14>  The valley of the Hackensack invited early settlers in the seventeenth century, and the valley of the Overpeck Creek, a navigable arm of the Hackensack, also attracted settlers quite as early in this direction.