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E. Goods transportation
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 pi units of goods. No more than si units of goods can be sold in the i-th city.

For each pair of cities i and j such that 1 ≤ i < 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.

Input

The first line of the input contains two integers n and c (1 ≤ n ≤ 10 000, 0 ≤ c ≤ 109) — the number of cities and the maximum amount of goods for a single transportation.

The second line contains n integers pi (0 ≤ pi ≤ 109) — the number of units of goods that were produced in each city.

The third line of input contains n integers si (0 ≤ si ≤ 109) — the number of units of goods that can be sold in each city.

Output

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

Examples
Input
3 0
1 2 3
3 2 1
Output
4
Input
5 1
7 4 2 1 0
1 2 3 4 5
Output
12
Input
4 3
13 10 7 4
4 7 10 13
Output
34