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.