Problem Statement

For a finite multiset S of non-negative integers, let us define $\mathrm{mex}(S)$ as the smallest non-negative integer not in S. For instance, $\mathrm{mex}(\lbrace 0,0, 1,3\rbrace ) = 2, \mathrm{mex}(\lbrace 1 \rbrace) = 0, \mathrm{mex}(\lbrace \rbrace) = 0$.
There are N non-negative integers on a blackboard. The i-th integer is A_i.
You will perform the following operation exactly K times.

• Choose zero or more integers on the blackboard. Let S be the multiset of chosen integers, and write $\mathrm{mex}(S)$ on the blackboard once.

How many multisets can be the multiset of integers on the final blackboard? Find this count modulo 998244353.

Input

The input is given from Standard Input in the following format:
N K
$A_1 A_2 \ldots A_N$

Output

Print the answer.

Constraints

• $1 \leq N,K \leq 2\times 10^5$
• $0\leq A_i\leq 2\times 10^5$
• All numbers in the input are integers.

Sample Input 1

3 1
0 1 3

Sample Output 1

3

The following three multisets can be obtained by the operations.

• $\lbrace 0,0,1,3 \rbrace$
• $\lbrace 0,1,1,3\rbrace$
• $\lbrace 0,1,2,3 \rbrace$

For instance, you can get $\lbrace 0,1,1,3\rbrace$ by choosing the 0 on the blackboard to let $S=\lbrace 0\rbrace$ in the operation.

Sample Input 2

2 1
0 0

Sample Output 2

2

The following two multisets can be obtained by the operations.

• $\lbrace 0,0,0 \rbrace$
• $\lbrace 0,0,1\rbrace$

Note that you may choose zero integers in the operation.

Sample Input 3

5 10
3 1 4 1 5

Sample Output 3

7109

见题面 Input 部分

见题面 Output 部分