CF923E.Perpetual Subtraction

There is a number x initially written on a blackboard. You repeat the following action a fixed amount of times:

1. take the number x currently written on a blackboard and erase it
2. select an integer uniformly at random from the range [0, x] inclusive, and write it on the blackboard

Determine the distribution of final number given the distribution of initial number and the number of steps.

黑板上最初写有一个数字 $x$。你将重复执行以下操作固定次数：

1. 擦去黑板上当前写的数字 $x$；
2. 在区间 $[0,\,x]$（含端点）中均匀随机地选取一个整数，并将其写在黑板上。

给定初始数字的分布以及操作步数，求最终数字的分布。

The first line contains two integers, N (1 ≤ N ≤ 105) — the maximum number written on the blackboard — and M (0 ≤ M ≤ 1018) — the number of steps to perform.

The second line contains N + 1 integers _P_0, _P_1, ..., P__N (0 ≤ P__i < 998244353), where P__i describes the probability that the starting number is i. We can express this probability as irreducible fraction P / Q, then . It is guaranteed that the sum of all _P__i_s equals 1 (modulo 998244353).

第一行包含两个整数 $N$（$1 \leq N \leq 10^5$）——黑板上可能出现的最大数字，以及 $M$（$0 \leq M \leq 10^{18}$）——需要执行的操作步数。

第二行包含 $N+1$ 个整数 $P_0,\,P_1,\,\dots,\,P_N$（$0 \leq P_i < 998244353$），其中 $P_i$ 表示初始数字为 $i$ 的概率。该概率可表示为最简分数 $P/Q$，则有 。保证所有 $P_i$ 的和模 $998244353$ 等于 $1$。

Output a single line of N + 1 integers, where R__i is the probability that the final number after M steps is i. It can be proven that the probability may always be expressed as an irreducible fraction P / Q. You are asked to output .

输出一行 $N+1$ 个整数，其中 $R_i$ 表示经过 $M$ 步后最终数字为 $i$ 的概率。可以证明该概率总能表示为最简分数 $P/Q$。你需要输出 。

In the first case, we start with number 2. After one step, it will be 0, 1 or 2 with probability 1/3 each.

In the second case, the number will remain 2 with probability 1/9. With probability 1/9 it stays 2 in the first round and changes to 1 in the next, and with probability 1/6 changes to 1 in the first round and stays in the second. In all other cases the final integer is 0.

第一种情况：我们从数字 2 开始。经过一步后，结果为 0、1 或 2 的概率各为 $1/3$。

第二种情况：数字在两步后仍为 2 的概率为 $1/9$；以概率 $1/9$，它在第一轮保持为 2，第二轮变为 1；以概率 $1/6$，它在第一轮变为 1，第二轮保持为 1。其余所有情况下，最终整数均为 0。