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: Runtime Error)

#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#include <deque>
#include <queue>
#include <array>
#include <set>
#include <map>
#include <cmath>
#include <complex>
#include <algorithm>
#include <numeric>
#include <utility>
#include <tuple>
#include <bitset>
#include <cstdint>
#include <cassert>
#include <random>
#include <iterator>

using namespace std;
using i64 = int64_t;
using i32 = int32_t;

int main() {
    const i64 mod = 998244353;
    i64 n, s;
    cin >> n >> s;
    vector<i64> a(n);
    for (int i = 0; i < n; ++i) cin >> a[i];
    vector<i64> dp(s + 1);
    i64 ans = 0, i = 1;
    for (i64 x : a) {
        for (i64 i = s - x; i > 0; --i) {
            dp[i + x] += dp[i];
            dp[i + x] %= mod;
        }
        dp[x] += i;
        ans += dp[s];
        ++i;
    }
    cout << ans << endl;
    return 0;
}