...The S value of an array is the sum of maximum values across all continuous subsequences length at least one. In the array (4,5,1), the value is 4+5+1+5+5+5=25.

You are given an array $$$A$$$ of length $$$N$$$. There are $$$N$$$ updates, where the $$$i$$$th value of the array is increased from by a value $$$B_i$$$.

Output $$$N+1$$$ integers, the S value after every update.

$$$N \leq 5 \cdot 10^5$$$