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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int, int> pi;
#define trace3(x, y, z) cerr << #x << ": " << x << ", " << #y < ": " << y << ", " << #z << ": " << z << endl;
#define all(v) v.begin(), v.end()
#define MOD 998244353

int main() {
	int n, s;
	cin >> n >> s;
	vi a(n + 1);
	for(int i = 1; i <= n; i++) cin >> a[i];
	vvll dp(n + 1, vll(s + 1, 0)), dpsum(n + 1, vll(s + 1, 0));
	for(int i = 1; i <= n; i++) {
		for(int j = 0; j <= s; j++) {
			if(a[i] == j) {
				dp[i][j] = i;
			}
			else if(a[i] < j) {
				dp[i][j] = dpsum[i - 1][j - a[i]];
			}
			(dpsum[i][j] = dpsum[i - 1][j] + dp[i][j]) %= MOD;
		}
	}
	ll ans = 0;
	for(int i = 1; i <= n; i++) {
		(ans += dp[i][s] * (n - i + 1)) %= MOD;
	}
	cout << ans << endl;
}