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
from collections import deque

line1 = raw_input().split()
line2 = [int(ai) for ai in raw_input().split()]

N = int(line1[0])
x = int(line1[1])

caught = [False] * N
time = 0

# FUNCTIONS

def catch_fast_ones():
    global N, x, line2, caught, time
    A = list(line2)
    while (min(A) < x):
        current_minimum = min(A)
        indices = [i for i, value in enumerate(line2) if value == current_minimum]

        already_caught_all = True

        for ind in indices:
            if not caught[ind]:
                already_caught_all = False
                break

        if not already_caught_all:
            occurrences = line2.count(current_minimum)
            time += (current_minimum * occurrences)

            for ind in indices:
                caught[ind] = True

        while (current_minimum in A):
            A.remove(current_minimum)


def cast_spell():
    global N, x, line2, caught, time
    time += x
    items = deque(caught)
    items.rotate(1)
    caught = list(items)


def all_caught():
    global N, x, line2, caught, time
    for value in caught:
        if not value:
            return False
    return True


def catch_all():
    global N, x, line2, caught, time
    for i in range(N):
        time += line2[i]

# MAIN:

if max(line2) < x:
    catch_all()
else:
    while not all(caught):
        catch_fast_ones()
        if not all(caught):
            cast_spell()

print time
