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;

const int N = 3003;
const int MOD = 998244353;

int n, s;
int a[N];

int dp[N][N];
int f(int x, int sum) {
  if (sum == 0) return x+2;
  if (x < 0 || sum < 0) return 0;
  if (~dp[x][sum]) return dp[x][sum];

  return dp[x][sum] = (f(x-1, sum) + f(x-1, sum - a[x])) % MOD;
}

int solve() {
  scanf("%d %d", &n, &s);
  for (int i = 0; i < n; ++i) {
    scanf("%d", &a[i]);
  }

  memset(dp, -1, sizeof dp);

  int ans = 0;
  for (int i = 0; i < n; ++i) {
    // cerr << f(i, s) << endl;
    ans = (ans + 1LL * f(i-1, s-a[i]) * (n-i)) % MOD;
  }

  printf("%d\n", ans);
  return 0;
}

int main() {
  int t = 1;
  // scanf("%d", &t);
  while (t--) solve();
  return 0;
}