4. The sequence $x_{1}, x_{2}, \cdots, x_{100}$ satisfies the following conditions: For $k=1,2, \cdots, 100, x_{k}$ is less than the sum of the other 99 numbers by $k$. Given that $x_{S 0}=\frac{m}{n}, m, n$ are coprime positive integers. Then $m+n$ equals $(\quad)$.
(A) 50
(B) 100
(C) 165
(D) 173