Devastating blow

Algebra Level 3

x2011+a1x2010+a2x2009++a2010+1 \large x^{2011} + a_{1}x^{2010} + a_{2} x^{2009} +\ldots + a_{2010} +1

Given x1,x2,x3,,x2011x_1 , x_2 , x_3 , \ldots , x_{2011} are the roots of the polynomial above and that y1=x1 x2x10y2=x2 x3x11y3=x3 x4x12y2011=x2011 x1 x2x9\begin{aligned} y_1 &=& x_{1} \ x_{2} \cdots x_{10} \\ y_2 &=& x_{2} \ x_{3} \cdots x_{11} \\ y_3 &=& x_{3} \ x_{4} \cdots x_{12} \\ &\cdot& \\ &\cdot& \\ &\cdot& \\ y_{2011} &=& x_{2011}\ x_{1} \ x_{2} \cdots x_{9} \end{aligned}

Find the value of (y1 y2y2011)20112010 {{(y_1 \ y_2\ldots y_{2011})}^{2011}}^{2010}.

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