Piegirl was asked to implement two table join operation for distributed database system, minimizing the network traffic. Suppose she wants to join two tables, A and B . Each of them has certain number of rows which are distributed on different number of partitions. Table A is distributed on the first cluster consisting of m partitions. Partition with index i has a i rows from A . Similarly, second cluster containing table B has n partitions, i -th one having b i rows from B . In one network operation she can copy one row from any partition to any other partition. At the end, for each row from A and each row from B there should be a partition that has both rows. Determine the minimal number of network operations to achieve this.

输入描述:

First line contains two integer numbers, m and n (1 ≤ m, n ≤ 105). Second line contains description of the first cluster with m space separated integers, ai(1 ≤ ai ≤ 109). Similarly, third line describes second cluster with n space separated integers, bi(1 ≤ bi ≤ 109).

输出描述:

Print one integer — minimal number of copy operations.

备注:

In the first example it makes sense to move all the rows to the second partition of the second cluster which is achieved in 2 + 6 + 3 = 11 operationsIn the second example Piegirl can copy each row from B to the both partitions of the first cluster which needs 2·3 = 6 copy operations.