MatKor Cup Seat Arrangement

This MatKor Cup has $N$ participants in total, and the contest hall has $M$ seats. Jongwoo assigned each of the $N$ participants a different seat in advance. Dongwoo asked Jongwoo how the seats were assigned.

Jongwoo would not simply tell him. Instead, he asked Dongwoo to predict the seat of each of the $N$ participants. Dongwoo chose $N$ different seats out of the $M$ seats, then predicted the seat of each participant.

For each $i$, find the probability that exactly $i$ of the $N$ predicted participants were predicted to sit in the same seat that Jongwoo assigned to them.

Jongwoo and Dongwoo assign and predict seats with equal probability over all possible cases.

The first line contains the number of participants and the number of seats, $N$ and $M$ ($1\le N\le M\le 5\,000\,000$), separated by a space.

Print the answer on a single line modulo $10^9+7$. Print $N+1$ numbers, from $i=0$ to $i=N$, separated by spaces. Note that you must print all $N+1$ values, from 0 to $N$, separated by spaces.

Let $\frac{p}{q}$ be an irreducible fraction with $p\ge 0$, $q>0$, and $\gcd(p,q)=1$. Its value modulo $M$ is $p\cdot q^{-1} \pmod M$, where $q^{-1}$ is the modular multiplicative inverse of $q$ modulo $M$, meaning $q\cdot q^{-1}\equiv 1 \pmod M$. If the fraction is an integer, then $q=q^{-1}=1$, so the value is $p \pmod M$.

It can be proven that under the given conditions, each probability is an integer or a rational number whose denominator is not a multiple of $10^9+7$.