Easy Task

Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB


Calculating the derivation of a polynomial is an easy task. Given a function f(x) , we use (f(x))' to denote its derivation. We use x^n to denote xn. To calculate the derivation of a polynomial, you should know 3 rules: (1) (C)'=0 where C is a constant. (2) (Cx^n)'=C*n*x^(n-1) where n>=1 and C is a constant. (3) (f1(x)+f2(x))'=(f1(x))'+(f2(x))'. It is easy to prove that the derivation a polynomial is also a polynomial. Here comes the problem, given a polynomial f(x) with non-negative coefficients, can you write a program to calculate the derivation of it?


Standard input will contain multiple test cases. The first line of the input is a single integer T (1 <= T <= 1000) which is the number of test cases. And it will be followed by T consecutive test cases. There are exactly 2 lines in each test case. The first line of each test case is a single line containing an integer N (0 <= N <= 100). The second line contains N + 1 non-negative integers, CN, CN-1, ..., C1, C0, ( 0 <= Ci <= 1000), which are the coefficients of f(x). Ci is the coefficient of the term with degree i in f(x). (CN!=0)


For each test case calculate the result polynomial g(x) also in a single line. (1) If g(x) = 0 just output integer 0.otherwise (2) suppose g(x)= Cmx^m+Cm-1x^(m-1)+...+C0 (Cm!=0),then output the integers Cm,Cm-1,...C0. (3) There is a single space between two integers but no spaces after the last integer.

Sample Input

3 2 1
10 0 1 2

Sample Output

6 2
30 0 1




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