Goods transportation

题面翻译

小明升任了 CF 国的大总管，他管辖的 $n$ 个城市，编号为 $1..n$ 。每个城市生产了 $p_i$ 个货物，限制最多可以卖掉 $s_i$ 个货物。对于每两个城市 $i, j$ ，如果 $i < j$ ，则可以最多从 $i$ 运送 $c$ 个货物到 $j$ 。注意不能反向运送，却可以在多个城市之间送来送去。现在小明想知道，经过运输后，最多能卖掉多少个货物。

感谢@larryzhong 提供的翻译

题目描述

There are $n$ cities located along the one-way road. Cities are numbered from $1$ to $n$ in the direction of the road.

The $i$ -th city had produced $p_{i}$ units of goods. No more than $s_{i}$ units of goods can be sold in the $i$ -th city.

For each pair of cities $i$ and $j$ such that 1<=i&lt;j<=n you can no more than once transport no more than $c$ units of goods from the city $i$ to the city $j$ . Note that goods can only be transported from a city with a lesser index to the city with a larger index. You can transport goods between cities in any order.

Determine the maximum number of produced goods that can be sold in total in all the cities after a sequence of transportations.

输入格式

The first line of the input contains two integers $n$ and $c$ ( $1<=n<=10000$ , $0<=c<=10^{9}$ ) — the number of cities and the maximum amount of goods for a single transportation.

The second line contains $n$ integers $p_{i}$ ( $0<=p_{i}<=10^{9}$ ) — the number of units of goods that were produced in each city.

The third line of input contains $n$ integers $s_{i}$ ( $0<=s_{i}<=10^{9}$ ) — the number of units of goods that can be sold in each city.

输出格式

Print the maximum total number of produced goods that can be sold in all cities after a sequence of transportations.

样例 #1

样例输入 #1

3 0
1 2 3
3 2 1

样例输出 #1

4

样例 #2

样例输入 #2

5 1
7 4 2 1 0
1 2 3 4 5

样例输出 #2

12

样例 #3

样例输入 #3

4 3
13 10 7 4
4 7 10 13

样例输出 #3

34