One of the tasks students routinely carry out in their mathematics classes is to solve a polynomial √ equation. It is, given a polynomial, say X2 − 4X + 1, to find its roots (2 ± 3). If the students’ task is to find the roots of a given polynomial, the teacher’s task is then to find a polynomial that has a given root. Ms. Galsone is an enthusiastic mathematics teacher who is bored with finding solutions of quadratic equations that are as simple as a + b c. She wanted to make higher- degree equations whose solutions are a little more complicated. As usual in problems in mathematics classes, she wants to maintain all coefficients to be integers and keep the degree of the polynomial as small as possible (provided it has the specified root). Please help her by writing a program that carries out the task of the teacher’s side. You are given a number t of the form: √
2/2 2. mn≤20 3. The coefficients of the answer a0, . . . , ad are between (−231 + 1) and (231 − 1), inclusive. Output For each dataset, output the coefficients of its minimal polynomial on integers F(X) = adXd + ad−1Xd−1 + · · · + a1X + a0, in the following format. ad ad−1 ... a1 a0 Non-negative integers must be printed without a sign (+ or -). Numbers in a single line must be separated by a single space and no other characters or extra spaces may appear in the output. Sample Input 3222 3223 2234 31 4 2 3 3227 0000 Sample Output 1 0 -10 0 1 1 0 -9 -4 27 -36 -23 1 0 -8 0 18 0 -104 0 1 1 0 0 -8 -93 0 24 -2976 2883 -32 -3720 -23064 -29775 1 0 -21 0 189 0 -945 -4 2835 -252 -5103 -1260 5103 -756 -2183