Box 1 contains three cards bearing numbers $1,2,3$; box 2 contains five cards bearing numbers $1,2,3,4,5$; and box 3 contains seven cards bearing numbers $1,2,3,4,5,6,7$. A card is drawn from each of the boxes. Let $x_i$ be the number on the card drawn from the $i^{\text{th}}$ box, $i = 1,2,3$.
The probability that $x_1 + x_2 + x_3$ is odd, is\\
(A) $\frac{29}{105}$\\
(B) $\frac{53}{105}$\\
(C) $\frac{57}{105}$\\
(D) $\frac{1}{2}$