CF1919F1.Wine Factory (Easy Version)

This is the easy version of the problem. The only difference between the two versions is the constraint on $c_i$ and $z$. You can make hacks only if both versions of the problem are solved.

There are three arrays $a$, $b$ and $c$. $a$ and $b$ have length $n$ and $c$ has length $n-1$. Let $W(a,b,c)$ denote the liters of wine created from the following process.

Create $n$ water towers. The $i$-th water tower initially has $a_i$ liters of water and has a wizard with power $b_i$ in front of it. Furthermore, for each $1 \le i \le n - 1$, there is a valve connecting water tower $i$ to $i + 1$ with capacity $c_i$.

For each $i$ from $1$ to $n$ in this order, the following happens:

1. The wizard in front of water tower $i$ removes at most $b_i$ liters of water from the tower and turns the removed water into wine.
2. If $i \neq n$, at most $c_i$ liters of the remaining water left in water tower $i$ flows through the valve into water tower $i + 1$.

There are $q$ updates. In each update, you will be given integers $p$, $x$, $y$ and $z$ and you will update $a_p := x$, $b_p := y$ and $c_p := z$. After each update, find the value of $W(a,b,c)$. Note that previous updates to arrays $a$, $b$ and $c$ persist throughout future updates.

这是该问题的简单版本。两个版本之间的唯一区别在于对 $c_i$ 和 $z$ 的约束条件。仅当两个版本的问题均被解决时，才允许进行 Hack。

给定三个数组 $a$、$b$ 和 $c$，其中 $a$ 和 $b$ 的长度为 $n$，而 $c$ 的长度为 $n-1$。记 $W(a,b,c)$ 为通过以下过程所生成的葡萄酒（单位：升）总量。

构建 $n$ 座水塔。第 $i$ 座水塔初始含有 $a_i$ 升水，且其前方有一位法力值为 $b_i$ 的巫师。此外，对每个 $1 \le i \le n - 1$，在第 $i$ 座与第 $i + 1$ 座水塔之间设有一个容量为 $c_i$ 的阀门。

按 $i = 1, 2, \dots, n$ 的顺序，依次对每座水塔执行如下操作：

1. 第 $i$ 座水塔前方的巫师最多从该塔中移除 $b_i$ 升水，并将所移除的水全部转化为葡萄酒；
2. 若 $i \neq n$，则第 $i$ 座水塔中剩余的水最多有 $c_i$ 升经由阀门流入第 $i + 1$ 座水塔。

共有 $q$ 次更新操作。每次更新给出整数 $p$、$x$、$y$ 和 $z$，并将 $a_p := x$、$b_p := y$、$c_p := z$。每次更新后，请计算并输出 $W(a,b,c)$ 的值。注意：对数组 $a$、$b$ 和 $c$ 所做的先前更新会持续生效，影响后续所有更新。

The first line contains two integers $n$ and $q$ ($2 \le n \le 5\cdot 10^5$, $1 \le q \le 5\cdot 10^5$) — the number of water towers and the number of updates.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 10^9$) — the number of liters of water in water tower $i$.

The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ($0 \le b_i \le 10^9$) — the power of the wizard in front of water tower $i$.

The fourth line contains $n - 1$ integers $c_1, c_2, \ldots, c_{n - 1}$ ($c_i \color{red}{=} 10^{18}$) — the capacity of the pipe connecting water tower $i$ to $i + 1$.

Each of the next $q$ lines contains four integers $p$, $x$, $y$ and $z$ ($1 \le p \le n$, $0 \le x, y \le 10^9$, $z \color{red}{=} 10^{18}$) — the updates done to arrays $a$, $b$ and $c$.

Note that $c_n$ does not exist, so the value of $z$ does not matter when $p = n$.

第一行包含两个整数 $n$ 和 $q$（$2 \le n \le 5\cdot 10^5$，$1 \le q \le 5\cdot 10^5$）—— 分别表示水塔的数量和更新操作的次数。

第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$0 \le a_i \le 10^9$）—— 表示第 $i$ 个水塔中所含的水量（单位：升）。

第三行包含 $n$ 个整数 $b_1, b_2, \ldots, b_n$（$0 \le b_i \le 10^9$）—— 表示位于第 $i$ 个水塔前方的巫师的法力值。

第四行包含 $n - 1$ 个整数 $c_1, c_2, \ldots, c_{n - 1}$（$c_i \color{red}{=} 10^{18}$）—— 表示连接第 $i$ 个水塔与第 $i + 1$ 个水塔的管道的容量。

接下来的 $q$ 行中，每行包含四个整数 $p$、$x$、$y$ 和 $z$（$1 \le p \le n$，$0 \le x, y \le 10^9$，$z \color{red}{=} 10^{18}$）—— 表示对数组 $a$、$b$ 和 $c$ 所做的更新操作。

注意：$c_n$ 不存在，因此当 $p = n$ 时，$z$ 的值无关紧要。

Print $q$ lines, each line containing a single integer representing $W(a, b, c)$ after each update.

输出 $q$ 行，每行包含一个整数，表示每次更新后的 $W(a, b, c)$ 值。

The first update does not make any modifications to the arrays.

• When $i = 1$, there are $3$ liters of water in tower 1 and $1$ liter of water is turned into wine. The remaining $2$ liters of water flow into tower 2.
• When $i = 2$, there are $5$ liters of water in tower 2 and $4$ liters of water is turned into wine. The remaining $1$ liter of water flows into tower 3.
• When $i = 3$, there are $4$ liters of water in tower 3 and $2$ liters of water is turned into wine. The remaining $2$ liters of water flows into tower 4.
• When $i = 4$, there are $5$ liters of water in tower 4. All $5$ liters of water are turned into wine.

Hence, $W(a,b,c)=1 + 4 + 2 + 5 = 12$ after the first update.

The second update modifies the arrays to $a = [3, 5, 3, 3]$, $b = [1, 1, 2, 8]$, and $c = [10^{18}, 10^{18}, 10^{18}]$.

• When $i = 1$, there are $3$ liters of water in tower 1 and $1$ liter of water is turned into wine. The remaining $2$ liters of water flow into tower 2.
• When $i = 2$, there are $7$ liters of water in tower 2 and $1$ liter of water is turned into wine. The remaining $6$ liters of water flow into tower 3.
• When $i = 3$, there are $9$ liters of water in tower 3 and $2$ liters of water is turned into wine. The remaining $7$ liters of water flow into tower 4.
• When $i = 4$, there are $10$ liters of water in tower 4. Only $8$ liters of water is turned into wine.

Hence, $W(a,b,c)=1 + 1 + 2 + 8 = 12$ after the second update.

The third update modifies the arrays to $a = [3, 5, 0, 3]$, $b = [1, 1, 0, 8]$, and $c = [10^{18}, 10^{18}, 10^{18}]$.

• When $i = 1$, there are $3$ liters of water in tower 1 and $1$ liter of water is turned into wine. The remaining $2$ liters of water flow into tower 2.
• When $i = 2$, there are $7$ liters of water in tower 2 and $1$ liter of water is turned into wine. The remaining $6$ liters of water flow into tower 3.
• When $i = 3$, there are $6$ liters of water in tower 3 and $0$ liters of water is turned into wine. The remaining $6$ liters of water flow into tower 4.
• When $i = 4$, there are $9$ liters of water in tower 4. Only $8$ liters of water is turned into wine.

Hence, $W(a,b,c)=1 + 1 + 0 + 8 = 10$ after the third update.

第一次更新不会对数组进行任何修改。

• 当 $i = 1$ 时，塔 1 中有 3 升水，其中 1 升水被转化为酒。剩余的 2 升水流向塔 2。
• 当 $i = 2$ 时，塔 2 中有 5 升水，其中 4 升水被转化为酒。剩余的 1 升水流向塔 3。
• 当 $i = 3$ 时，塔 3 中有 4 升水，其中 2 升水被转化为酒。剩余的 2 升水流向塔 4。
• 当 $i = 4$ 时，塔 4 中有 5 升水，全部 5 升水均被转化为酒。

因此，第一次更新后，$W(a,b,c)=1 + 4 + 2 + 5 = 12$。

第二次更新将数组修改为 $a = [3, 5, 3, 3]$，$b = [1, 1, 2, 8]$，以及 $c = [10^{18}, 10^{18}, 10^{18}]$。

• 当 $i = 1$ 时，塔 1 中有 3 升水，其中 1 升水被转化为酒。剩余的 2 升水流向塔 2。
• 当 $i = 2$ 时，塔 2 中有 7 升水，其中 1 升水被转化为酒。剩余的 6 升水流向塔 3。
• 当 $i = 3$ 时，塔 3 中有 9 升水，其中 2 升水被转化为酒。剩余的 7 升水流向塔 4。
• 当 $i = 4$ 时，塔 4 中有 10 升水，其中仅有 8 升水被转化为酒。

因此，第二次更新后，$W(a,b,c)=1 + 1 + 2 + 8 = 12$。

第三次更新将数组修改为 $a = [3, 5, 0, 3]$，$b = [1, 1, 0, 8]$，以及 $c = [10^{18}, 10^{18}, 10^{18}]$。

• 当 $i = 1$ 时，塔 1 中有 3 升水，其中 1 升水被转化为酒。剩余的 2 升水流向塔 2。
• 当 $i = 2$ 时，塔 2 中有 7 升水，其中 1 升水被转化为酒。剩余的 6 升水流向塔 3。
• 当 $i = 3$ 时，塔 3 中有 6 升水，其中 0 升水被转化为酒。剩余的 6 升水流向塔 4。
• 当 $i = 4$ 时，塔 4 中有 9 升水，其中仅有 8 升水被转化为酒。

因此，第三次更新后，$W(a,b,c)=1 + 1 + 0 + 8 = 10$。