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B. Producing Snow

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAlice 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*.

Examples

Input

3

10 10 5

5 7 2

Output

5 12 4

Input

5

30 25 20 15 10

9 10 12 4 13

Output

9 20 35 11 25

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.

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