Let \(r_1,\) \(r_2,\) \(\dots,\) \(r_7\) be the distinct complex roots of the polynomial \(P(x) = x^7 - 7.\) Let
\(K = \prod_{1 \le i < j \le 7} (r_i + r_j).\)
In other words, \(K\) is the product of all numbers of the of the form \(r_i+r_j,\) where \(i\) and \(j\) are integers for which \(1 \le i < j \le 7.\) Determine \(K^2.\)
