CF1809F.Traveling in Berland

There are $n$ cities in Berland, arranged in a circle and numbered from $1$ to $n$ in clockwise order.

You want to travel all over Berland, starting in some city, visiting all the other cities and returning to the starting city. Unfortunately, you can only drive along the Berland Ring Highway, which connects all $n$ cities. The road was designed by a very titled and respectable minister, so it is one-directional — it can only be traversed clockwise, only from the city $i$ to the city $(i \bmod n) + 1$ (i.e. from $1$ to $2$, from $2$ in $3$, ..., from $n$ to $1$).

The fuel tank of your car holds up to $k$ liters of fuel. To drive from the $i$-th city to the next one, $a_i$ liters of fuel are needed (and are consumed in the process).

Every city has a fuel station; a liter of fuel in the $i$-th city costs $b_i$ burles. Refueling between cities is not allowed; if fuel has run out between cities, then your journey is considered incomplete.

For each city, calculate the minimum cost of the journey if you start and finish it in that city.

伯兰德有 $n$ 座城市，它们呈环形排列，并按顺时针方向编号为 $1$ 到 $n$。

你想环游整个伯兰德：从某座城市出发，访问其余所有城市，最后返回出发城市。不幸的是，你只能沿伯兰德环形高速公路行驶，该公路连接全部 $n$ 座城市。这条公路由一位极富声望且备受尊敬的部长设计，因此是单向的——仅允许顺时针通行，即仅能从城市 $i$ 驾车前往城市 $(i \bmod n) + 1$（即从 $1$ 到 $2$，从 $2$ 到 $3$，……，从 $n$ 到 $1$）。

你的汽车油箱最多可容纳 $k$ 升燃油。从第 $i$ 座城市驶向下一座城市需消耗 $a_i$ 升燃油（并在行驶过程中被完全消耗）。

每座城市均设有加油站；在第 $i$ 座城市购买 1 升燃油的价格为 $b_i$ 伯尔（burles）。城市之间不允许加油；若在两城之间燃油耗尽，则视为旅程失败。

对每座城市，请计算以该城市为起点和终点完成整个旅程所需的最低花费。

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains two integers $n$ and $k$ ($3 \le n \le 2 \cdot 10^5$; $1 \le k \le 10^9$) — the number of cities and the volume of fuel tank, respectively.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le k$).

The third line contains $n$ integers $b_1, b_2, \dots, b_n$ ($1 \le b_i \le 2$).

The sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。

每个测试用例的第一行包含两个整数 $n$ 和 $k$（$3 \le n \le 2 \cdot 10^5$；$1 \le k \le 10^9$）—— 城市数量和油箱容量。

第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \le a_i \le k$）。

第三行包含 $n$ 个整数 $b_1, b_2, \dots, b_n$（$1 \le b_i \le 2$）。

所有测试用例的 $n$ 之和不超过 $2 \cdot 10^5$。

For each test case, print $n$ integers, where the $i$-th of them is equal to the minimum cost of the journey if you start and finish in the $i$-th city.

对于每个测试用例，输出 $n$ 个整数，其中第 $i$ 个整数表示从第 $i$ 个城市出发并最终回到第 $i$ 个城市的旅程的最小花费。