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 ll long long
#define N 2000

int n, c, a[N + 5], b[N + 5];
ll ans = 0x7f7f7f7f7f7f7f7f;

int main() {
	scanf("%d%d", &n, &c);
	for (int i = 0; i < n; ++i)
		scanf("%d", &a[i]);
	memset(b, 0x3f, sizeof b);
	for (int t = 0; t < n; ++t) {
		ll sum = 0;
		for (int i = 0; i < n; ++i) {
			b[i] = min(b[i], a[(i - t + n) % n]);
			sum += b[i];
		}
		ans = min(ans, sum + 1LL * t * c);
	}
	printf("%lld\n", ans);
	return 0;
}