You are given \(N+1\) distinct positive integers \(A_1,A_2,......,A_{N+1}\) and a positive integer \(M\). A polynomial of degree \(N\) is defined as follows: 

\(f(x)= P_1x^N + P_2x^{N-1} + ……..+ P_Nx + P_{N+1} \)

such that following conditions hold true:

• \(f(A_i) = A_i^{N+1} \ \forall i\in [1,N+1]\)

• \(P_1 > 0\)

• \(P_1,P_2,.....,P_{N+1}\) are integers

A new polynomial is defined as

\(S(x) = X_1x^N + X_2x^{N-1} + ……..+ X_Nx + X_{N+1} \)

Such that \(X_i = |P_i|\%M \ \ \forall i\in [1,N+1]\) and \(X_1,X_2,.......,X_{N+1}\) are integers.

Evaluate \(S(0)\%M, S(1)\%M ,…….S(M-1)\%M\) .

Input format

• First line: Two space separated integers \(N\) and \(M\)
• Second line: \(N+1\) space separated integers \(A_1,A_2,......,A_{N+1}\)

Output format

• Output \(M\) space-separated integers \(S(0)\%M, S(1)\%M ,…….S(M-1)\%M\)

Constraints

\(1 \le N,M, A_i \le 10^5\)

\(M\) is prime

Subtasks

• For 20 Points: \(1 \le N,M, A_i \le 1000\)
• For 80 Points: Original constraints