Problem Statement

Roy needs to count the number of "good sequences" defined as follows: Elements: The sequence must contain only odd integers. Sum Condition: The sum of the sequence must equal X. Prefix Sum Condition: The cumulative sums (prefix sums) of the sequence should not match any of the elements in the array A=[A1,A2,...,AN]. Given the potentially large count of good sequences, return the result modulo 998244353. Input Format First line of input contains two integers N and X representing the number of elements in given array A and given sum respectively. Second line of input contains N integers A1, A2, ..., AN which are elements of given array A. Output Format Single line of output contains an integer which is the count of good sequences by taking mod with 998244353. Constraints 1 ≤ N ≤ 10 2 1 ≤ X ≤ 10 18 1 ≤ A1,A2,...AN ≤ 10 18 Sample Testcase 1 Testcase Input 2 4 1 3 Testcase Output 0 Explanation In the second test case, we need odd integer sequences summing to 4, with cumula