Binomial Coefficients Modulo p

Problem Description

Given a prime $p$ and an integer $n$, for each $r = 0, 1, \dots, p - 1$, count how many pairs $(i, j)$ with $0 \le j \le i \le n$ satisfy $\binom{i}{j} \equiv r \pmod p$.

Input Format

The first line contains two integers $n, p$.

Output Format

Output one line of $p$ numbers, the answers for $r = 0, 1, \dots, p - 1$.

Sample Input

114 7

Sample Output

4012 900 273 450 315 276 444

Constraints

For all test cases, $2 \le p \le 100$, $1 \le n \le 10^9$, and $p$ is prime.