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.