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.

Input

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

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

Note

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.