It can be proved that the value is a rational number
Bobo knows that int_{0}^{infty} frac{1}{1 + x^2} mathrm{d}x = frac{pi}{2}. ∫ ∞ 1+x 2 1 dx= 2 π . Given n distinct positive integers a_1, a_2, dots, a_n a 1 ,a 2 ,…,a n , find the value of frac{1}{pi} int_{0}^{infty} frac{1}{prod_{i = 1}^n(a_i^2 + x^2)} mathrm{d}x. π 1 ∫ ∞ ∏ i=1 n (a i 2 +x 2 ) 1 dx. It can be proved that the value is a rational number frac{p}{q} q p . Print the result as (p cdot q^{-1}) bmod (10^9+7) (p⋅q −1 )mod(10 9 +7).
（图片来源网络，侵删）
