Problem:


Score : 400 points

Problem Statement

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.

Sample Input 1

2 10
1 100

Sample Output 1

12

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Cast the spell. The color of the slime changes: 1 → 2. This takes 10 seconds.

Catch a slime in color 1. This takes 1 second.

Sample Input 2

3 10
100 1 100

Sample Output 2

23

Snuke can act as follows:

Catch a slime in color 2. This takes 1 second.

Cast the spell. The color of the slime changes: 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Cast the soell. The color of each slime changes: 3 → 1, 2 → 3. This takes 10 seconds.

Catch a slime in color 2. This takes 1 second.

Sample Input 3

4 10
1 2 3 4

Sample Output 3

10

Snuke can act as follows:

Catch a slime in color 1. This takes 1 second.

Catch a slime in color 2. This takes 2 seconds.

Catch a slime in color 3. This takes 3 seconds.

Catch a slime in color 4. This takes 4 seconds.



Sample input:
2 10
1 100


Sample output:
12

Submission status: Runtime Error

Solution code:
N, x = list(map(int, input().split()))
a = list(map(int, input().split()))
min_index = a.index(min(a))
index_list = list(range(min_index,N)) + list(range(min_index))
cost = a.copy()
c_count = [0]*N
for i in range(1,N):
    if cost[index_list[i]] => (cost[index_list[i-1]]+x):
        cost[index_list[i]] = cost[index_list[i-1]]+x
        c_count[index_list[i]] = c_count[index_list[i-1]]+1

print(sum(cost) - sum(c_count)*x + max(c_count)*x  )

Submission status: Runtime Error

Solution code:
n, x = map(int, raw_input().split())
A = map(int, raw_input().split())*2
ans = 10**18
for l in xrange(1, n+1):
    deq = [0]*n
    s = t = 0
    res = 0
    for i in xrange(n):
        while s<t and A[deq[t-1]] >= A[i]:
            t -= 1
        deq[t] = i
        t += 1
        if deq[s] == i-l+1:
            s += 1
    for i in xrange(n, 2*n):
        while s<t and A[deq[t-1]] >= A[i]:
            t -= 1
        deq[t] = i
        t += 1

        res += A[deq[s]]

        if deq[s] == i-l+1:
            s += 1
    ans = min(ans, res+x*(l-1))
print ans

Submission status: Runtime Error

Solution code:
ef cast(curr, num):
    arr = [(x+num) % N for x in curr]
    return arr


def transform(curr, val):
    ret = 0
    while ((val-ret + N) % N) in curr:
        ret += 1
    return ret

N, x = map(int, raw_input().split())
a = map(int, raw_input().split())

curr = []
ans = 0
while len(curr) < N:
    cost = list(a)
    t = map(lambda x: transform(curr, x), range(N))
    for i in range(N):
        cost[i] += t[i] * x
    pick = cost.index(min(cost))
    curr = cast(curr, t[pick])
    ans += cost[pick]
    curr.append(pick)

print ans