A group of school leavers had their graduation party at an aquapark. They had a great time, but when they were leaving the aquapark they were surprised by a suddenly cold weather and a heavy rain, which made it quite a problem to get to the trolleybus stop.

It turned out that all the boys in the company had their umbrellas and all the girls were without umbrellas. Of course, each boy, being a real gentleman, volunteered to accompany one of the girls to the trolleybus stop under his umbrella.

If the ith girl gets wet under the rain, she'll get upset by g_i units. If no girl accepts an invitation from the jth boy, he'll get upset by b_j · k units, where k is the number of luckier boys who will accompany girls under their umbrellas. The girls who will go under umbrellas and the accompanying boys will not get upset at all.

Help the boys and girls keep their holiday mood as unspoiled as possible. Determine how they should proceed to make the total upset minimal.

The first line contains the number of girls n and boys m in the group (1 ≤ n, m ≤ 100). The second line contains the girls' upsets g₁, …, g_n separated with a space. The third line contains the boys' upset coefficients b₁, …, b_m separated with a space. The numbers in the second and third lines are positive integers not exceeding 1000.

Output the minimal possible total upset.