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<iostream>
#include<algorithm>
#include<vector>
#define LL long long
#define PP std::pair<LL,LL>
int N;
LL a[5010];
LL d[5010];
LL x;
LL ans = 1000000000000000000;
int main() {
	std::cin >> N >> x;
	for (int i = 1; i <= N; i++) {
		std::cin >> a[i];
		a[i + N] = a[i];
		d[i] = 1 << 30;
	}
	for (int i = 0; i <= N; i++) {
		LL sum = i * x;
		for (int j = 1; j <= N; j++) {
			d[j] = std::min(d[j], a[j + N - i]);
			sum += d[j];
		}
		ans = std::min(ans, sum);
	}
	std::cout << ans << std::endl;
	return 0;
}