Problem:
Score : 600 points

Problem Statement

Given are a sequence of N integers A_1, A_2, \ldots, A_N and a positive integer S.

For a pair of integers (L, R) such that 1\leq L \leq R \leq N, let us define f(L, R) as follows:

f(L, R) is the number of sequences of integers (x_1, x_2, \ldots , x_k) such that L \leq x_1 < x_2 < \cdots < x_k \leq R and A_{x_1}+A_{x_2}+\cdots +A_{x_k} = S.

Find the sum of f(L, R) over all pairs of integers (L, R) such that 1\leq L \leq R\leq N. Since this sum can be enormous, print it modulo 998244353.

Constraints

All values in input are integers.

1 \leq N \leq 3000

1 \leq S \leq 3000

1 \leq A_i \leq 3000

Input

Input is given from Standard Input in the following format:

N S
A_1 A_2 ... A_N

Output

Print the sum of f(L, R), modulo 998244353.

Sample Input 1

3 4
2 2 4

Sample Output 1

5

The value of f(L, R) for each pair is as follows, for a total of 5.

f(1,1) = 0

f(1,2) = 1 (for the sequence (1, 2))

f(1,3) = 2 (for (1, 2) and (3))

f(2,2) = 0

f(2,3) = 1 (for (3))

f(3,3) = 1 (for (3))

Sample Input 2

5 8
9 9 9 9 9

Sample Output 2

0

Sample Input 3

10 10
3 1 4 1 5 9 2 6 5 3

Sample Output 3

152

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sa = br.readLine().split(" ");
		int n = Integer.parseInt(sa[0]);
		int s = Integer.parseInt(sa[1]);
		sa = br.readLine().split(" ");
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(sa[i]);
		}
		br.close();

		int mod = 998244353;
		long ans = 0;
		int[][] dp = new int[n + 1][s + 1];
		dp[0][0] = 1;
		for (int i = 0; i < n; i++) {
			for (int j = 0; j <= s; j++) {
				dp[i + 1][j] += dp[i][j];
				if (j == 0) {
					dp[i + 1][a[i]] += i + 1;
				} else {
					if (j + a[i] <= s) {
						dp[i + 1][j + a[i]] += dp[i][j];
					}
				}
			}
		}
//		for (int i = 0; i < dp.length; i++) {
//			for (int j = 0; j < dp[i].length; j++) {
//				System.out.print(dp[i][j] + "\t");
//			}
//			System.out.println();
//		}
		for (int i = 1; i <= n; i++) {
			ans += (dp[i][s] - dp[i - 1][s]) * (n - i + 1) % mod;
		}
		ans %= mod;
		System.out.println(ans);
	}
}