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>

typedef long long ll;

const int kN = 2e3 + 5;

ll a[kN], c[kN];

int main() {
	int n; ll ans = 0, x;
	scanf("%d%lld", &n, &x);
	for(int i = 1; i <= n; ++i) scanf("%lld", a + i), c[i] = a[i], ans += a[i];
	for(int i = 1; i <= n; ++i) {
		ll cur_cost = x * i;
		for(int j = 1; j <= n; ++j) {
			c[j] = std::min(c[j], a[(j + i - 1) % n + 1]);
			cur_cost += c[j];
		}
		ans = std::min(cur_cost, ans);
	}
	printf("%lld", ans);
	return 0;
}