# Sum of Sums

**Number Theory**Level pending

Many people know the story of Gauss, and how he came up with a method to sum up consecutive integers. However, what many people donâ€™t know is the story of Steelfirez. One day, Steelfirez's particularly cruel teacher (even more so than Gauss') gave him the following problem: Given that \(S_{1}(N) = \sum\limits_{x=1}^{N}x\) and \(S_{k}(N) = \sum\limits_{x=1}^{N}S_{k-1}(x)\), for \(k>1\), what is the closed form of \(S_{k}(N)\)? Steelfirez, having nothing better to do, worked hard and managed to come up with a solution. In honor of Steelfirez's hard work, we ask you to find the maximum positive integer \(p\), such that \(S_{2014}(2014)\equiv0 \ (mod \ 10^p)\).

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