CF923B.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.

爱丽丝非常喜欢雪！不幸的是，今年的冬天已经结束了，她再也无法期待下雪了。于是鲍勃送给她一份礼物——一台大型造雪机。他计划每天制造一定量的雪。在第 $i$ 天，他会制造体积为 $V_i$ 的一堆雪，并将其堆放在她的花园里。

每天，每一堆雪都会因融化而略微缩小。更准确地说，若某天的温度为 $T_i$，则每堆雪的体积将减少 $T_i$。如果这一减少会使某堆雪的体积降至零或以下，则该堆雪将永远消失。所有雪堆彼此独立。

注意：第 $i$ 天制造的雪堆，在当天就会开始损失部分体积。在极端情况下，这可能导致某天结束时花园中已无任何雪堆剩余。

现给出每天初始雪堆的体积以及每天的温度，请计算每一天融化的雪的总体积。

The first line contains a single integer N (1 ≤ N ≤ 105) — the number of days.

The second line contains N integers _V_1, _V_2, ..., V__N (0 ≤ V__i ≤ 109), 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 ≤ 109), where T__i is the temperature on the day i.

第一行包含一个整数 $N$（$1 \leq N \leq 10^5$）—— 表示天数。

第二行包含 $N$ 个整数 $V_1,\ V_2,\ ..., \ V_N$（$0 \leq V_i \leq 10^9$），其中 $V_i$ 表示第 $i$ 天所堆雪堆的初始体积。

第三行包含 $N$ 个整数 $T_1,\ T_2,\ ..., \ T_N$（$0 \leq T_i \leq 10^9$），其中 $T_i$ 表示第 $i$ 天的温度。

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

输出一行，包含 N 个整数，其中第 i 个整数表示第 i 天融化的雪的总体积。

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.

在第一个样例中，鲍勃首先堆了一个体积为 10 的雪堆，该雪堆在当天融化至体积 5。第二天，他又堆了一个体积为 10 的雪堆。由于当天比前一天稍暖，第一个雪堆完全消失，而第二个雪堆缩小至体积 3。第二天结束时，他仅剩一个体积为 3 的雪堆。第三天，他堆的雪堆比平时小，但由于气温也下降了，两个雪堆均存活至当天结束。