Problem Statement

You are given a sequence of length $N$, $A = (A_1, ..., A_N)$, and an integer $K$.
How many permutations of $A$ are there such that no two adjacent elements sum to less than $K$? Find the count modulo $998244353$.

Constraints

• $2 \\leq N \\leq 2 \\times 10^5$
• $0 \\leq K \\leq 10^9$
• $0 \\leq A_i \\leq 10^9$
• All values in the input are integers.

Input

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

$N$ $K$ $A_1$ $A_2$ $\\dots$ $A_N$

Output

Print the answer.

Sample Input 1

4 5
1 2 3 4

Sample Output 1

4

The following four permutations satisfy the condition:

• $(1, 4, 2, 3)$
• $(1, 4, 3, 2)$
• $(2, 3, 4, 1)$
• $(3, 2, 4, 1)$

Sample Input 2

4 3
1 2 3 3

Sample Output 2

12

There are $12$ permutations of $A$, all of which satisfy the condition.

Sample Input 3

10 7
3 1 4 1 5 9 2 6 5 3

Sample Output 3

108