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.conv, std.math, std.string, std.range, std.array,
       std.algorithm;

void main(){
    auto buf = readln().strip().split().map!(to!long)();
    immutable N = buf[0];
    immutable x = buf[1];

    auto a = readln().strip().split().map!(to!long)().array();

    auto cost = a.dup;
    auto shift = new long[](N);

    for (size_t i = 0; i < N; ++i) {
        for (size_t j = 1; j < N; ++j) {
            auto n = a[i] + x*j;
            auto p = (i+j)%N;
            if(cost[p] > n) {
                cost[p] = n;
                shift[p] = cast(long)j;
            }
        }
    }

    long take;
    for (size_t i = 0; i < N; ++i) {
        take += cost[i] - shift[i] * x;
    }

    writeln(shift.reduce!max * x + take);
}
