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.

Input

The input is given from Standard Input in the following format:
N M
$C_1 \ldots C_M$

Output

Print the answer.

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.

Sample Input 1

2 2
1 1

Sample Output 1

3

The series of operations may proceed as follows:

• You draw a card with 1 written on it. The notebook now has one 1 written in it.
• You again draw a card with 1 written on it. The notebook now has two 1s written in it.
• You draw a card with 2 written on it. The notebook now has two 1s and one 2 written in it.

The sought expected value is $2\times\frac{1}{2}+3\times\frac{1}{4}+4\times\frac{1}{8}+\ldots=3$.

Sample Input 2

5 2
4 1

Sample Output 2

748683270

The expected value is $\frac{21}{4}, whose representation modulo 998244353$ is 748683270.

Sample Input 3

50 50
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Sample Output 3

244742906

The expected value is $\frac{13943237577224054960759}{61980890084919934128}$.

Sample Input 4

74070 15
1 2 3 11 22 33 111 222 333 1111 2222 3333 11111 22222 33333

Sample Output 4

918012973

见题面 Input 部分

见题面 Output 部分