Let's consider so called "sly number" which is given as an array A of N integers from set {0,1,2}. For example A[0]=1, A[1]=1, A[2]=0 and A[3]=2. A sly number is called ONE, if A[0]=1 and A[I]=0 for I=1,2,?,N-1.
Consider following operation with two sly numbers A and B called 'Star Multiplication':

k N-1 C[k] = ∑ A[i] * B[k-i] + ∑ A[i] * B[N+k-i]. i=0 i=k+1here C ? the result of the operation, even also presented in an array - not necessarily sly number. This operation we will denote by <*> symbol. Moreover, there is also module operation over the results of 'Star Multiplication':

(C mod Q) [i] = C[i] mod Q,where Q is a positive integer. We are given a sly number A and a module Q. We need to find such 'inverse sly number' B: (A * B) mod Q = ONE.

The input contains K data sets in text format. The first line of this file contains the number K of test cases. Each test consists of two lines. First line contains two integers separated by spaces: Q (2 <= Q <= 100) and N (5 <= N <= 50). Second line contains N integers from set {0,1,2} separated by spaces, which present sly number A.

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