Max the monke has been sent to the store to grab some bananas. There are ~N~ types of bananas, each with a size ~s_i~ and an infinite supply. Max wants to fill his backpack with bananas. If Max's backpack can hold bananas with total size at most ~M~, how many ways can he fill his backpack? Note that the order of the items in his backpack matters.

Input Specification

The first line of the input contains two integers ~N,M\ (1 \leq N \leq M \leq 2\cdot 10^5)~.

The second line will contain ~N~ integers ~s_i\ (1 \leq s_i \leq M)~.

Output Specification

On one line you are to print the number of ways he can fill his backpack modulo ~998244353~.

Subtasks

Subtask 1 (5%)

~M \leq 2000~

Subtask 2 (95%)

No further constraints.

Sample Input

2 5
1 2

Sample Output

8