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
using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
class Program
{       
    public void Slove()
    {
        var inputs = Console.ReadLine().Split();
        int n = int.Parse(inputs[0]);
        long shiftCost = long.Parse(inputs[1]);
        long[] costs = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long minSum = costs.Sum();
        foreach(int i in Enumerable.Range(1, n))
        {
            long temp = costs[n - 1];
            foreach(int j in Enumerable.Range(1, n - 1))
            {
                costs[j] = Math.Min(costs[j], costs[j - 1]);
            }
            costs[0] = Math.Min(costs[0], temp);
            minSum = Math.Min(minSum, costs.Sum() + shiftCost * i);
        }
        System.Console.WriteLine(minSum);
    }
    
    static void Main(string[] args)
    {
        new Program().Slove();
    }
}
