Hamster's Summation Challenge

Given two integers n and x, and a sequence of n+1 integers a₀, a₁, ..., a_n, define

S_k(x)=\( \sum_{i=0}^{x} i^k \) ,

with the special definition that \(0^0=1\) (i.e. when i=0 and k=0, treat it as 1). You are to compute

\( \sum_{k=0}^{n} S_k(x) \times a_k \).

Note: It is guaranteed that the values of n and x are relatively small (at most 1000), so a simple iterative solution will suffice.

inputFormat

The input consists of two lines:

• The first line contains two integers n and x, where n (0 ≤ n ≤ 1000) denotes the highest power index and x (0 ≤ x ≤ 1000) is the upper limit of summation.
• The second line contains n+1 integers: a₀, a₁, ..., a_n.

outputFormat

Output a single integer representing the value of \( \sum_{k=0}^{n} S_k(x) \times a_k \).

sample

1 2
1 1

6