Water deposits

There are $n$ water deposits in a line. They are so huge that they can be considered to have infinite capacity. Initially, each deposit $i$ has $\ell_i$ liters in it. You have a pump that you can use to transfer water from any deposit $i$ to any adjacent deposit ( $i - 1$ or $i + 1$ ). Each use of the pump to transfer water between two deposits has cost $p + \ell$ , where $p$ is a constant cost to connect two adjacent deposits, and $\ell$ is the number of liters transferred. Your goal is to minimize the cost to equally distribute the water among all the deposits.

Input

Input consists of several cases, each with $n$ and $p$ , followed by $\ell_1, \dots, \ell_n$ . You can assume $1 \le n \le 10^5$ , $0 \le p \le 10^9$ , $0 \le \ell_i \le 10^9$ , and that the sum of all $\ell_i$ ’s is a multiple of $n$ .

Output

For each case, print the minimum cost to equally distribute the water among all the deposits.

Problem information

Author: Jordi Cortadella

Generation: 2026-01-25T11:07:01.207Z