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
#include <bits/stdc++.h>

#define int long long

using namespace std;

int b[100001];
int a[100001];

 main () {
    int n, m;
    cin >> n >> m;
    for (int i = 1;i <= n + n;i ++) b[i] = 1e9 + 7;
    for (int i = 1;i <= n;i ++) cin >> a[i];
    for (int i = 1;i <= n;i ++) a[i + n] = a[i];
    int ans = 1e9 + 7;
    for (int k = 0;k <= n;k ++) {
        int cur = k * m;
    	for (int i = n + 1;i <= n + n;i ++) {
			b[i] = min (b[i], a[i - k]);
			cur += b[i]; 
    	}
    	ans = min (ans, cur);
    }
    cout << ans;
    return 0;
}