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
import std.stdio, std.string, std.conv;
import std.algorithm, std.array;
 
auto solve(string s_)
{
    auto Nx = s_.split.map!(to!int)();
    immutable N=Nx[0], x=Nx[1];
    auto as = readln.split.map!(to!int).array();
    int m=sum(as);
    foreach(k;1..N)
    {
        auto dp = new int[N];
        foreach(i;0..N) dp[i]=min(as[i],as[(i-1+N)%N]);
        m=min(m,sum(dp)+x*k);
        swap(dp,as);
    }
    return m;
}

void main(){ for(string s; (s=readln.chomp()).length;) writeln(solve(s)); }