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.range, std.algorithm, std.array, std.typecons, std.container;
import std.math, std.numeric, core.bitop;

enum inf3 = 1_001_001_001;
enum inf6 = 1_001_001_001_001_001_001L;
enum mod = 1_000_000_007L;


void main() {
    int n, x;
    scan(n, x);
    auto a = readln.split.to!(long[]);

    long amin = inf3;
    int s;

    foreach (i ; 0 .. n) {
        if (amin > a[i]) {
            amin = a[i];
            s = i;
        }
    }

    long ans = amin;
    long p = amin;
    int l, ml;
    int t = s;

    foreach (i ; 1 .. n) {
        if (a[(s + i) % n] > p + x) {
            l++;
            p += x;
        }
        else {
            t = (s + i) % n;
            p = a[t];
            l = 0;
        }
        ans += a[t];
        ml = max(l, ml);
    }

    ans += 1L * ml * x;

    writeln(ans);
}









void scan(T...)(ref T args) {
    import std.stdio : readln;
    import std.algorithm : splitter;
    import std.conv : to;
    import std.range.primitives;

    auto line = readln().splitter();
    foreach (ref arg; args) {
        arg = line.front.to!(typeof(arg));
        line.popFront();
    }
    assert(line.empty);
}

void fillAll(R, T)(ref R arr, T value) {
    static if (is(typeof(arr[] = value))) {
        arr[] = value;
    }
    else {
        foreach (ref e; arr) {
            fillAll(e, value);
        }
    }
}
