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>
#define rep(i,n)for(int i=0;i<n;i++)
using namespace std;
typedef long long ll;
typedef pair<int, int>P;

ll a[4002];

int main() {
	ll n, x; scanf("%lld%lld", &n, &x);
	for (ll i = 0; i < n; i++) {
		scanf("%lld", &a[i]);
		a[n + i] = a[i];
	}
	sort(a, a + n, greater<>());
	ll ans = LLONG_MAX;
	ll cnt;
	for (ll i = 0; i < n; i++) {
		cnt = x*i;
		for (ll j = 0; j < n; j++) {
			if (j < i)cnt += a[n - 1];
			else cnt += a[j];
		}
		ans = min(ans, cnt);
		cnt = x*i;
	}
	printf("%lld\n", ans);
	return 0;
}