Problem Statement

There are $N$ cards in a box. Each card has an integer written on it, which is between $1$ and $M$, inclusive. For each $i=1,\ldots,M$, there are $C_i$ cards with the number $i$ written on them.

Starting with an empty notebook, you repeat the following operation:

• Randomly draw one card from the box. Write the integer on the card in the notebook, then return the card to the box.

Find the expected value, modulo $998244353$, of the number of times the operation is performed until the notebook has all integers from $1$ to $M$ written at least once.

How to find an expected value modulo $998244353$ The expected value sought in this problem can be proven to always be a rational number. Furthermore, the constraints of this problem guarantee that when the expected value is expressed as an irreducible fraction $\frac yx$, the denominator $x$ is not divisible by $998244353$. Then, there is a unique $0\leq z\lt998244353$ such that $y\equiv xz\pmod{998244353}$. Print this $z$.

Constraints

• $1 \leq M \leq N \leq 2\times 10^5$
• $1 \leq C_i$
• $\sum_{i=1}^{M}C_i=N$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N M
C_1 \ldots C_M

Output

Print the answer.