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