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.array, std.string, std.conv, std.algorithm;
import std.typecons, std.range, std.random, std.math, std.container;
import std.numeric, std.bigint, core.bitop;

void main() {
    auto s = readln.split;
    auto N = s[0].to!int;
    auto X = s[1].to!long;
    auto A = readln.split.map!(to!long).array;


    int rot = 0;
    long ans = 0;
    foreach (i; 0..N) {
        long tmp = A[i];
        int max_j = i;
        foreach (j; 1..N) {
            if (A[(i-j+N)%N] + j * X <= tmp) {
                tmp = A[(i-j+N)%N] + j * X;
                max_j = (i-j+N)%N;
            }
        }
        rot = max(rot, max_j);
        ans += A[max_j];
    }

    writeln(ans + rot * X);
}
