Starting with \(S= 0 \), you choose a number between \(0\) and \(1\) at random and add it to \(S\). If \( S< 1 \), you repeat and choose a number between \(0\) and \(1\) at random and add it to \(S\). If \(S \geq 1 \), you stop.

If the expected value of \(S\) when you stop is denoted by \( E[S]\), what is the integer closest to \[ \frac { 200 \times E[S] }{ e^2 } ? \]

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