Problem Statement

Given is an integer $N$.

Snuke is going to do the procedure below.

• Let $x$ be a variable and initialize it with a random integer between $0$ and $N$ (inclusive). For each $0 \leq i \leq N$, $x=i$ is chosen with probability $A_i/10^9$.
• Repeat the following operation $K$ times.
• With probability $x/N$, decrease the value of $x$ by $1$; with probability $1-x/N$, increase it by $1$. (Here, note that $x$ will still be between $0$ and $N$ after the operation.)

For each $i=0,1,\cdots,N$, find the probability, modulo $998244353$, that $x=i$ after the procedure.

Definition of probability modulo $998244353$ It can be proved that the sought probabilities are always rational numbers. Additionally, under the Constraints of this problem, when representing each of them as an irreducible fraction $\frac{P}{Q}$, it can be proved that $Q \neq 0 \pmod{998244353}$. Thus, there uniquely exists an integer $R$ such that $R \times Q \equiv P \pmod{998244353}, 0 \leq R < 998244353$. Answer with this $R$.

Constraints

• $1 \leq N \leq 100000$
• $0 \leq A_i$
• $\sum_{0 \leq i \leq N}A_i = 10^9$
• $1 \leq K \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_0 A_1 \cdots A_N

Output

For each $i=0,1,\cdots,N$, print the probability, modulo $998244353$, that $x=i$ after the procedure.