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 ll = long long;
constexpr ll inf = static_cast<ll>(1e15);
constexpr ll mod = static_cast<ll>(1e9 + 7);

int n;
ll a[2005], x;
ll b[2005];
int main()
{
	std::cin >> n >> x;
	for (int i = 0; i < n; ++i) {
		std::cin >> a[i];
		b[i] = inf;
	}

	ll ans = inf;
	for (int i = 0; i < n; ++i) {
		ll memo = 0;
		for (int j = 0; j < n; ++j) {
			b[j] = std::min(b[j], a[(n + (j - i)) % n]);
			memo += b[j];
		}
		ans = std::min(ans, memo + i * x);
	}
	std::cout << ans << std::endl;
	return 0;
}
