Problem Statement

We have $N$ boxes numbered $1$ to $N$. Initially, Box $i$ contains $A_i$ balls.

You will repeat the following operation $K$ times.

• Choose one box out of the $N$ uniformly at random (each time independently). Add one ball to the chosen box.

Let $B_i$ be the number of balls in Box $i$ after the $K$ operations, and the score be the product of the numbers of balls, $\\prod_{i=1}^{N}B_i$.

Find the expected value of the score modulo $998244353$.

Notes

When the expected value in question is represented as an irreducible fraction $p/q$, there uniquely exists an integer $r$ such that $rq\\equiv p \\pmod{998244353}$ and $0\\leq r < 998244353$ under the Constraints of this problem. This $r$ is the value we seek.

Constraints

• $1 \\leq N \\leq 1000$
• $1 \\leq K \\leq 10^9$
• $0 \\leq A_i \\leq 10^9$

Input

Input is given from Standard Input in the following format:

$N$ $K$ $A_1$ $\\ldots$ $A_N$

Output

Print the answer.

Sample Input 1

3 1
1 2 3

Sample Output 1

665496245

After the operation, the score will be as follows.

• When choosing Box $1$ in the operation, $2\\times 2\\times 3=12$.
• When choosing Box $2$ in the operation, $1\\times 3\\times 3=9$.
• When choosing Box $3$ in the operation, $1\\times 2\\times 4=8$.

Therefore, the expected value in question is $\\frac{1}{3}(12+9+8)=\\frac{29}{3}$. This value modulo $998244353$ is $665496245$.

Sample Input 2

2 2
1 2

Sample Output 2

499122182

After the operations, the score will be as follows.

• When choosing Box $1$ in the first operation and Box $1$ in the second, $3\\times 2=6$.
• When choosing Box $1$ in the first operation and Box $2$ in the second, $2\\times 3=6$.
• When choosing Box $2$ in the first operation and Box $1$ in the second, $2\\times 3=6$.
• When choosing Box $2$ in the first operation and Box $2$ in the second, $1\\times 4=4$.

Therefore, the expected value in question is $\\frac{1}{4}(6+6+6+4)=\\frac{11}{2}$.

Sample Input 3

10 1000000000
998244350 998244351 998244352 998244353 998244354 998244355 998244356 998244357 998244358 998244359

Sample Output 3

138512322