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
package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

const COST_MAX = 1000000000

func main() {
	sc := bufio.NewScanner(os.Stdin)
	for sc.Scan() {
		// one line
		l := sc.Text()
		t := strings.Split(l, " ")
		n, _ := strconv.Atoi(t[0])
		x, _ := strconv.Atoi(t[1])

		// two line
		sc.Scan()
		l = sc.Text()
		t = strings.Split(l, " ")
		c := make([]int, len(t))
		for idx, u := range t {
			c[idx], _ = strconv.Atoi(u)
		}

		totalCost := 0
		for i := 0; i < n; i++ {
			cost := COST_MAX
			for l := 0; l < n; l++ {
				foo := 0
				if i == l {
					foo = c[l]
				} else {
					foo = abs(i-l)*x + c[l]
				}
				// Find min cost
				if cost > foo {
					cost = foo
				}
			}

			totalCost += cost
		}

		fmt.Println(totalCost)
	}
}

func abs(n int) int {
	if n < 0 {
		return n * -1
	}
	return n
}