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>
using namespace std;
 
#define for_(i,a,b) for(int i=(a);i<(b);++i)
typedef long long lint;
 
int N;
lint x, a[2020];
 
int main() {
	cin >> N >> x;
	for_(i,0,N) cin >> a[i];
	
	vector< lint > min_a(N, 1 << 30);
	lint ans = 1LL << 60;
	
	for_(k,0,N) {
		lint ans_k = 0;
		for_(i,0,N) ans_k += (min_a[i] = min(min_a[i], a[(i - k + N) % N]));
		ans = min(ans, ans_k + (lint)k * x);
	}
	
	cout << ans << endl;
}