Polynomial Remainders

You are given the polynomial

a(x) = a_n x^n + ... + a_1 x + a_0.

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

The input consists of several test cases. The first line of each test case contains two integers n and k. (0 <= n, k <= 10000)

The next line contains n+1 coefficients of a(x), separated by spaces. The coefficients are given in order from a_0 through a_n.

The input ends when n = k = -1.

For each test case, output the coefficients of the remainder polynomial on one line, starting with the constant coefficient r_0.

If the remainder is 0, print only one constant coefficient. Otherwise, if the remainder has degree d, print exactly the d+1 coefficients from r_0 through r_d. Separate adjacent coefficients with a single space.

You may assume every coefficient of the remainder can be represented as a 32-bit integer.