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.

Examples

Input

2 10
1 100


Output

12


Input

3 10
100 1 100


Output

23


Input

4 10
1 2 3 4


Output

10
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 readln(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[left(i),j-1]}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.