A11667. Producing Snow

Alice likes snow a lot! Unfortunately, this year's winter is already over, and she can't expect to have any more of it. Bob has thus bought her a gift — a large snow maker. He plans to make some amount of snow every day. On day $i$ he will make a pile of snow of volume $V_{i}$ and put it in her garden.

Each day, every pile will shrink a little due to melting. More precisely, when the temperature on a given day is $T_{i}$ , each pile will reduce its volume by $T_{i}$ . If this would reduce the volume of a pile to or below zero, it disappears forever. All snow piles are independent of each other.

Note that the pile made on day $i$ already loses part of its volume on the same day. In an extreme case, this may mean that there are no piles left at the end of a particular day.

You are given the initial pile sizes and the temperature on each day. Determine the total volume of snow melted on each day.

The first line contains a single integer $N$ ( $1<=N<=10^{5}$ ) — the number of days.

The second line contains $N$ integers $V_{1},V_{2},...,V_{N}$ ( $0<=V_{i}<=10^{9}$ ), where $V_{i}$ is the initial size of a snow pile made on the day $i$ .

The third line contains $N$ integers $T_{1},T_{2},...,T_{N}$ ( $0<=T_{i}<=10^{9}$ ), where $T_{i}$ is the temperature on the day $i$ .

Output a single line with $N$ integers, where the $i$ -th integer represents the total volume of snow melted on day $i$ .

In the first sample, Bob first makes a snow pile of volume 10, which melts to the size of 5 on the same day. On the second day, he makes another pile of size 10. Since it is a bit warmer than the day before, the first pile disappears completely while the second pile shrinks to 3. At the end of the second day, he has only a single pile of size 3. On the third day he makes a smaller pile than usual, but as the temperature dropped too, both piles survive till the end of the day.