Bessie has N (2≤N≤300) tiles in a line with ugliness values a1,a2,…,aN in that order (1≤ai≤106). K(0≤K≤min(N,6)) of the tiles are stuck in place; specifically, those at indices x1,…,xK(1≤x1<x2<⋯<xK≤N).
Bessie wants to minimize the total ugliness of the tiles, which is defined as the sum of the maximum ugliness over every consecutive pair of tiles; that is, 
She is allowed to perform the following operation any number of times: choose two tiles, neither of which are stuck in place, and swap them.
Determine the minimum possible total ugliness Bessie can achieve if she performs operations optimally.
INPUT FORMAT (input arrives from the terminal / stdin):
The first line contains N and K.
The next line contains a1,…,aN .
The next line contains the K indices x1,…,xK.
OUTPUT FORMAT (print output to the terminal / stdout):
Output the minimum possible total ugliness.
SAMPLE INPUT:
3 0
1 100 10
SAMPLE OUTPUT:
110
Bessie can swap the second and third tiles so that a=[1,10,100], achieving total ugliness max(1,10)+max(10,100)=110. Alternatively, she could swap the first and second tiles so that a=[100,1,10], also achieving total ugliness max(100,1)+max(1,10)=110.
SAMPLE INPUT:
3 1
1 100 10
3
SAMPLE OUTPUT:
110
Bessie could swap the first and second tiles so that a=[100,1,10]
, achieving total ugliness max(100,1)+max(1,10)=110.
SAMPLE INPUT:
3 1
1 100 10
2
SAMPLE OUTPUT:
200
The initial total ugliness of the tiles is max(1,100)+max(100,10)=200
. Bessie is only allowed to swap the first and third tiles, which does not allow her to reduce the total ugliness.
SAMPLE INPUT:
4 2
1 3 2 4
2 3
SAMPLE OUTPUT:
9
SCORING:
Input 5: K=0
Inputs 6-7: K=1
Inputs 8-12: N≤50
Inputs 13-24: No additional constraints
Problem credits: Benjamin Qi
扫码领取USACO试题答案+详细解析
咨询一对一备赛规划
