Let ~V_i~ be the volatility of students ~1 \dots i~. The volatility of a set of students is simply the number of students ~i~ who cannot be coerced into using their phones by anybody else (in other words, the number of students ~i~ for which there exists no student ~j~ such ~S_i < S_j~ and ~D_j-R_j \le D_i \le D_j+R_j~). We can thus think of each student as contributing either ~0~ or ~1~ volatility to each ~V~ value. Let ~M_i~ be the smallest value of ~j~ which satisfies the above conditions (or ~M_i = N+1~ if there's no such ~j~). If ~M_i \le i~, then student ~i~ contributes no volatility at all, and otherwise, they contribute ~1~ volatility to each of the values ~V_{i \dots (M_i-1)}~. So, if we had the values ~M_{1 \dots N}~, we could use them to compute the volatilities ~V_{1 \dots N}~ with a simple ~\mathcal O(N)~ sweep.

What remains is computing the values ~M_{1 \dots N}~ efficiently. Let's process the ~N~ students in decreasing order of ~S~ value, either by explicitly sorting them by their ~S~ values, or by keying them by their ~S~ values and then iterating over all possible ~S~ values from ~10^6~ down to ~1~. Let ~X_d~ be the minimum index (in the original ordered student list) of any student processed so far whose range of influence includes desk ~d~ (or ~X_d = \infty~ if there's been no such student so far). When processing student ~i~, we can observe that ~M_i~ must be equal to ~X_{Pi}~. And upon finishing with student ~i~, we should update ~X_d~ to ~\min(X_d, i)~ for each desk ~d~ in the inclusive interval ~[D_i-R_i, D_i+R_i]~.

Let's maintain the values ~X_{1 \dots K}~ (where ~K~ is the maximum possible ~D~ value) using a segment tree with lazy propagation, in which each node stores the minimum value of any ~X~ value in its interval, as well as the minimum new value which all ~X~ values in its interval should lazily be updated with. This allows us to both query an ~X~ value and update a range of ~X~ values as necessary in ~\mathcal O(\log K)~ time each, resulting in an overall time complexity of ~\mathcal O((N \log K)+Z)~ (where ~K~ is the maximum possible ~D~ value and ~Z~ is the maximum possible ~S~ value).