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 <stdio.h>

int N; long long X,A[2020],U[2020];

int main()
{
	scanf ("%d %lld",&N,&X);
	for (int i=0;i<N;i++) scanf ("%lld",&A[i]);
	long long ans = 0;
	for (int i=0;i<N;i++) ans += A[i], U[i] = A[i];
	for (int i=1;i<N;i++){
		long long now = i * X;
		for (int j=0;j<N;j++){
			int k = (j + N - i) % N;
			if (U[j] > A[k])
				U[j] = A[k];
			now += U[j];
		}
		if (ans > now)
			ans = now;
	}
	printf ("%lld\n",ans);

	return 0;
}