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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;
using ll = long long;
const int N = 3005;

const int mod = 998244353;
int add(int a, int b) {
	return a + b < mod ? a + b : a + b - mod;
}

int n, s;
int a[N];

int dp[N][N];

int f(int i, int j) {
	if(j < 0) return 0;
	if(j == 0) return n - i + 1;
	if(i == n) return 0;
	int &ans = dp[i][j];
	if(~ans) return ans;
	return ans = add(f(i + 1, j), f(i + 1, j - a[i]));
}


int main() {
	memset(dp, -1, sizeof dp);
	scanf("%d %d", &n, &s);

	for(int i = 0; i < n; i++) scanf("%d", a + i);

	int ans = 0;

	for(int i = 0; i < n; i++) {
		ans = add(ans, f(i, s));
	}

	printf("%d\n", ans);
}