CareerCup

Next Sunday is Ayan’s 4th birthday and a lot of guests are invited for his birthday celebration. All of them are getting gifts for Ayan and his y-1 number of siblings. There are x number of guests coming to the party and each of them presented each kid some integer number of gifts (possibly zero). The guests are numbered with integers from 1 to x and all kids are numbered with integers from 1 to y. For all 1 ≤i ≤x the minimum number of gifts, which i-th guest presented to some kid is equal to gi and for all 1 ≤j ≤y the maximum number of gifts, which j-th kid received from some guest is equal to kj.

Let ai,j be the number of gifts which the i-th guest give to the j-th kid. Then gi is equal exactly to the minimum among values ai,1,ai,2,…,ai,y and kj is equal exactly to the maximum among values g1,j,g2,j,…,gx,j.



You are interested in the minimum total number of gifts that guests could present, so you need to minimize the sum of ai,j for all (i,j) such that 1 ≤i ≤x and 1 ≤j ≤y. You are given the numbers g1,…,gx and k1,…,ky, determine this number.

Input Format

The first line contains two integers x and y, separated with space — the number of guests and kids, respectively (2≤x,y≤100000). The second line contains x integers g1,…,gx, separated by spaces — gi is equal to the minimum number of gifts, which i-th guest presented to some kid (0≤gi≤1000). The third line contains y integers k1,…,ky, separated by spaces — kj is equal to the maximum number of gifts, which j-th kid received from some guest (0≤kj≤1000).

Output Format

If the described situation is impossible, print −1. In another case, print the minimum total number of gifts, which guests could have presented and all conditions could have satisfied.

Sample Input

3 2

1 2 1

3 4

Sample Output

12

Mr. Stark is the owner of Stark industries, a manufacturer of weaponry.

A local Mafia group has hijacked one of the factories in the desert.

The mafias want to transport the weapons from the factory to their base camp, and use a single truck to do it.

But, every kilometer the truck travels with the weapons, one weapon falls off and breaks. The truck can only travel integral values of distance, and will lose 1 weapon for every km travelled.

The weapons can be unloaded at any point from the truck, and can be picked up again later.

Given the number of weapons X, max capacity of the truck Y and distance between the factory and the base Z, find the maximum number of weapons that can be transferred intact from the factory to the mafia base.



Function Description:

findMaxWeapons function takes the following parameters:

X - the number of weapons

Y - max capacity of the truck

Z - distance between the factory and the base

A string can contain only a, b or c. There cannot be 2 consecutive same character. First and the last character cannot be the same. Now given a string with ‘a’, ‘b’, ‘c’ or ‘?’. We need to find the string replacing ‘?’ that satisfy the above conditions. For multiple-answer display lexicographically smallest string. For no answer possible display “Not Possible”.