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(ll i=0;i<n;i++)
using namespace std;
typedef long long ll;

ll a[2000], b[2000];
int main() {
	ll n, x; scanf("%lld%lld", &n, &x);
	rep(i, n) { scanf("%lld", &a[i]); b[i] = a[i]; }
	ll ans = LLONG_MAX;
	rep(i, n) {
		ll cnt = 0;
		rep(j, n) { b[j] = min(b[j], a[(j + n - i) % n]); cnt += b[j]; }
		ans = min(ans, cnt + i*x);
	}
	printf("%lld\n", ans);
}