Given a polynomial and a number t, please convert it into an equivalent polynomial in the form of .

The input contains several test cases.
The first line of each test case gives two integer n (1 < n ≤ 200) and t (-10 ≤ t ≤ 10). The following line is a sequence of n integer a₀,a₁, ... ,a_n (-1000 ≤ a_i ≤ 1000), which is separated by exactly one space.

For each test case, output the equivalent polynomial's coefficient b₀,b₁, ... ,b_n. One line for each test case and each number is separated by exactly one space, no extra space at the end of each line.

2 1
1 0 2

3 4 2