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