Laser Chaos

Bob has placed $n$ laser shooters on the infinitely long number line. The $i-th$ laser shooter is placed at position $a_i$ and has a power level of $b_i$. When the $i-th$ shooter is triggered, it destroys everything to its left within distance $b_i$. The shooter is itself not destroyed. If the laser from the $i-th$ shooter hits another shooter $j (j < i)$, then the $j-th$ shooter is destroyed and