Problem:
Score : 400 points

Problem Statement

Snuke lives in another world, where slimes are real creatures and kept by some people.
Slimes come in N colors. Those colors are conveniently numbered 1 through N.
Snuke currently has no slime. His objective is to have slimes of all the colors together.

Snuke can perform the following two actions:

Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.

Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.

Find the minimum time that Snuke needs to have slimes in all N colors.

Constraints

2≤N≤2,000

a_i are integers.

1≤a_i≤10^9

x is an integer.

1≤x≤10^9

Input

The input is given from Standard Input in the following format:

N x
a_1 a_2 ... a_N

Output

Find the minimum time that Snuke needs to have slimes in all N colors.

Sample Input 1

2 10
1 100

Sample Output 1

12

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Cast the spell. The color of the slime changes: 1 → 2. This takes 10 seconds.

Catch a slime in color 1. This takes 1 second.

Sample Input 2

3 10
100 1 100

Sample Output 2

23

Snuke can act as follows:

Catch a slime in color 2. This takes 1 second.

Cast the spell. The color of the slime changes: 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Cast the soell. The color of each slime changes: 3 → 1, 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Sample Input 3

4 10
1 2 3 4

Sample Output 3

10

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Catch a slime in color 2. This takes 2 seconds.

Catch a slime in color 3. This takes 3 seconds.

Catch a slime in color 4. This takes 4 seconds.

Solution in Pascal (FPC 2.6.2) (judge verdict: Accepted)

var f:array[0..2000,0..2000] of int64;
    a:array[1..2000] of int64;
    n,i,j:longint;
    tot,minn,x:int64;
function left(k:longint):longint;
begin
  exit(((k-2+n) mod n)+1);
end;
function min(a,b:int64):int64;
begin
  if a<b then exit(a);
  exit(b);
end;
begin
  minn:=100000000000000000;
  readln(n,x);
  for i:=1 to n do read(a[i]);
  for i:=1 to n do f[i,0]:=a[i];
  for j:=1 to n-1 do
    for i:=1 to n do
      f[i,j]:=min(f[i,j-1],f[left(i),j-1]);
  for i:=0 to n-1 do
  begin
    tot:=x*i;
    for j:=1 to n do tot:=tot+f[j,i];
    if tot<minn then minn:=tot;
  end;
  writeln(minn);
end.