Question: Name the school that joined the Big 12 between 2010 and 2013 but also was the only school in the nation in 2007 to win a BCS game, a NCAA Men's Basketball Tournament game, and a NCAA Women's Basketball Tournament game

The West Virginia Mountaineers are the athletic teams that represent West Virginia University.  The school is a member of National Collegiate Athletic Association Division I.  At that time, the Mountaineers joined the Mid-American Conference as an affiliate member for men's soccer.  The two major sports at the university are football (played at Mountaineer Field at Milan Puskar Stadium) and basketball (played at the WVU Coliseum), although many of the other sports have large followings as well.  The Mountaineers have been a member of the Big 12 Conference since 2012.  The West Virginia University athletic program also has the honor of being the only school in the nation in 2007 to win a BCS game, a NCAA Men's Basketball Tournament game, and a NCAA Women's Basketball Tournament game. <SEP> The 2009–10 Baylor Bears basketball team represented Baylor University in the 2009–10 NCAA Division I men's basketball season.  This was head coach Scott Drew's seventh season at Baylor.  The Bears compete in the Big 12 Conference and played their home games at the Ferrell Center.  They advanced to the semifinals of the 2010 Big 12 Men's Basketball Tournament before losing to Kansas State.  They received an at–large bid to the 2010 NCAA Men's Division I Basketball Tournament, earning a #3 seed in the South Region.  Their first round win over #14 seed Sam Houston State was the school's first tournament win since 1950.  They defeated #11 seed Old Dominion in second round to advance to the Sweet Sixteen for the first time in school history.  They extended their record breaking run by defeating #10 seed Saint Mary's to advance to the Elite Eight where they would fall to #1 seed and AP #3 Duke.  They finished the season with a record of 28–8, the 28 wins is a school record. <SEP>  In all four schools have departed (Colorado, Missouri, Nebraska, Texas A&M) and two have joined (West Virginia, TCU) The 2010–13 Big 12 Conference realignment refers to the Big 12 Conference (Big 12) dealing with several proposed and actual conference expansion and reduction plans among various NCAA conferences and institutions.  Part of the larger NCAA conference realignment, beginning in the 2010-11 academic year and continuing to the present, the Big 12 was one of the more severely impacted conferences. <SEP> The 2010–11 VCU Rams men's basketball team represented Virginia Commonwealth University in the Colonial Athletic Association conference during the 2010–11 NCAA Division I men's basketball season.  The Rams, led by second year head coach Shaka Smart, played their home games at the Stuart C. Siegel Center.  They finished the season 28–12, 12–6 in CAA play and lost in the championship game of the 2011 CAA Men's Basketball Tournament to Old Dominion.  They received an at-large bid in the 2011 NCAA Men's Division I Basketball Tournament where they played in the new "First Four" round, defeating Southern California.  They defeated Georgetown and Purdue in the second and third rounds, respectively, to advance to the "Sweet Sixteen".  The defeated Florida State to advance to the "Elite Eight" where they defeated Kansas.  They advanced to the school's first ever "Final Four", being just the third 11 seed in Tournament history to advance to the "Final Four", where they were defeated by Butler.  The VCU Rams finished 6th in the ESPN/USA Today Coaches Poll at the end of the season.  This was the highest ranking in VCU's history and the highest ranking of any team from the CAA.  The 2011 NCAA tournament run by VCU is regarded as one of the best Cinderella runs of all time.  To date, they are the only men's Division I basketball team whose NCAA tournament journey ran from The First Four to the Final Four.  They are also the only team in the tournament to win five games, and not qualify for the national championship game.