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 thanc 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 andc (1≤n≤10000, 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.