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

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.