# What now? Minimum? Complicating...

Consider all sequences of positive real numbers \( x_i \), \( i = 1,2, \ldots, 333 \) that satisfy \( \sum_{i=1}^{333} x_i = 1 \). The minimum value of

\( \sum_{i=1}^{333} \frac{x_i}{1+\sum_{i \neq j, j=1}^{333} x_j} \)

is \( M \). Let \( M = \frac{a}{b} \). Find the value of \( a+b \).