22010_PolynomialRemains

Given the polynomial

a(x) = a_n xⁿ + ... + a₁ x + a₀,

compute the remainder r(x) when a(x) is divided by x^k+1.

The input consists of a number of cases. The first line of each case specifies the two integers n and k (0 ≤ n, k ≤ 10000). The next n+1 integers give the coefficients of a(x), starting from a₀ and ending with a_n. The input is terminated if n = k = -1.

For each case, output the coefficients of the remainder on one line, starting from the constant coefficient r₀. If the remainder is 0, print only the constant coefficient. Otherwise, print only the first d+1 coefficients for a remainder of degree d. Separate the coefficients by a single space.

You may assume that the coefficients of the remainder can be represented by 32-bit integers.

5 2
6 3 3 2 0 1
5 2
0 0 3 2 0 1
4 1
1 4 1 1 1
6 3
2 3 -3 4 1 0 1
1 0
5 1
0 0
7
3 5
1 2 3 4
-1 -1

3 2
-3 -1
-2
-1 2 -3
0
0
1 2 3 4