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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分