设数列\(\{ a_{n}\}\)的前\(n\)项和为\(S_{n}\)，令\({{T}_{n}}=\dfrac{{{S}_{1}}+{{S}_{2}}+\cdot \cdot \cdot +{{S}_{n}}}{n}\)，称\(T_{n}\)为数列\(a_{1}{,}a_{2}{,}{…}{,}a_{n}\)的“理想数”，已知数列\(a_{1}{,}a_{2}{,}{…}{,}a_{502}\)的“理想数”为\(2012\)，那么数列\(2{,}a_{1}{,}a_{2}{,}{…}{,}a_{502}\)的“理想数”为\((\ \ \ \ \ \ \ \ \ {  })\)