Problem:
Score : 500 points

Problem Statement

On an xy plane, in an area satisfying 0 ≤ x ≤ W, 0 ≤ y ≤ H, there is one house at each and every point where both x and y are integers.

There are unpaved roads between every pair of points for which either the x coordinates are equal and the difference between the y coordinates is 1, or the y coordinates are equal and the difference between the x coordinates is 1.

The cost of paving a road between houses on coordinates (i,j) and (i+1,j) is p_i for any value of j, while the cost of paving a road between houses on coordinates (i,j) and (i,j+1) is q_j for any value of i.

Mr. Takahashi wants to pave some of these roads and be able to travel between any two houses on paved roads only. Find the solution with the minimum total cost.

Constraints

1 ≦ W,H ≦ 10^5

1 ≦ p_i ≦ 10^8(0 ≦ i ≦ W-1)

1 ≦ q_j ≦ 10^8(0 ≦ j ≦ H-1)

p_i (0 ≦ i ≦ W−1) is an integer.

q_j (0 ≦ j ≦ H−1) is an integer.

Input

Inputs are provided from Standard Input in the following form.

W H
p_0
:
p_{W-1}
q_0
:
q_{H-1}

Output

Output an integer representing the minimum total cost.

Sample Input 1

2 2
3
5
2
7

Sample Output 1

29

It is enough to pave the following eight roads.

Road connecting houses at (0,0) and (0,1)

Road connecting houses at (0,1) and (1,1)

Road connecting houses at (0,2) and (1,2)

Road connecting houses at (1,0) and (1,1)

Road connecting houses at (1,0) and (2,0)

Road connecting houses at (1,1) and (1,2)

Road connecting houses at (1,2) and (2,2)

Road connecting houses at (2,0) and (2,1)

Sample Input 2

4 3
2
4
8
1
2
9
3

Sample Output 2

60

Solution in Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program gridian_mst
  implicit none
  integer :: w, h, i, a, b
  integer(8) :: c(200000,2), m
  c = 0_8
  read(*,*) w, h
  do i = 1, w
    read(*,*) c(i,1)
    c(i,2) = -1_8
  end do
  do i = w+1, w+h
    read(*,*) c(i,1)
    c(i,2) = 1_8
  end do
  call quick_sort(c(1:w+h,1:2),1)
  a = w+1
  b = h+1
  m = 0_8
  do i = 1, w+h
    if (c(i,2).lt.0_8) then
      if (a.eq.0) cycle
      m = m+c(i,1)*int(b,8)
      a = a-1
    else
      if (b.eq.0) cycle
      m = m+c(i,1)*int(a,8)
      b = b-1
    end if
  end do
  write(*,'(i0)') m
  stop
contains
  recursive subroutine quick_sort(a,i)
    implicit none
    integer(8), intent(inout) :: a(:,:)
    integer, intent(in) :: i
    integer(8) p, c(size(a(1,:)))
    integer :: n, l, r
    n = size(a(:,1))
    l = 1
    r = n
    p = a((l+r)/2,i)+a(l,i)+a(r,i)-max(a((l+r)/2,i),a(l,i),a(r,i))-min(a((l+r)/2,i),a(l,i),a(r,i))
    do
      do while (a(l,i).lt.p)
        l = l+1
      end do
      do while (a(r,i).gt.p)
        r = r-1
      end do
      if (l.ge.r) exit
      c = a(l,:)
      a(l,:) = a(r,:)
      a(r,:) = c
      l = l+1
      r = r-1
    end do
    if (l.gt.2) call quick_sort(a(1:l-1,:),i)
    if (n.gt.r+1) call quick_sort(a(r+1:n,:),i)
    return
  end subroutine quick_sort
end program gridian_mst