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 *i*th girl gets wet under the rain, she'll get upset by *g*_{i} units. If no girl accepts an
invitation from the *j*th 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.

### Input

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 *g*_{1}, …, *g*_{n} separated with a space. The third line
contains the boys' upset coefficients *b*_{1}, …, *b*_{m} separated with a space. The numbers in the second
and third lines are positive integers not exceeding 1000.

### Output

Output the minimal possible total upset.

### Sample

input | output |
---|

2 4
1 100
10 8 6 4
| 19 |

**Problem Author: **Sofia Tekhazheva, prepared by Denis Dublennykh

**Problem Source: **Ural Regional School Programming Contest 2010