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: Wrong Answer)

#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

#include <bits/stdc++.h>
/*#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>*/
 
#define pll              pair <long long,long long>
#define pb               push_back
#define ll               long long
#define ff               first
#define ss               second
#define D(x)             cerr<<#x " = "<<(x)<<endl
#define vll              vector <ll>
#define IOS              ios_base::sync_with_stdio(0); cin.tie(NULL);
#define endl             '\n'   
using namespace std;
const ll N = 3e3+1;
const ll S = 3e3+1;
ll dp[N][S];
ll a[N];
ll n,s;
int main()
{
    IOS
 	// freopen("input.txt","r",stdin);
 	// freopen("output.txt","w",stdout);
 	// freopen("error.txt","w",stderr);
 	memset(dp,0,sizeof(dp));
 	cin>>n>>s;
 	for(ll i=1;i<=n;i++)
 	{
 		cin>>a[i];
 	}	
 	//dp[0][0]=1;
 	ll ans=0;
 	for(ll i=1;i<=n;i++)
 	{
 		dp[i][a[i]]+=i;
 		for(ll j=0;j<N;j++)
 		{	
 			dp[i][j]+=dp[i-1][j];
 			if(j+a[i]<N)
 			{
 				dp[i][j+a[i]]+=dp[i-1][j];
 			}
 		}
 		// 	cout<<endl;
 		// for(ll j=0;j<=s;j++)
 		// {
 		// 	cout<<j<<" "<<dp[i][j]<<endl;
 		// }
 		ans+=(dp[i][s]-dp[i-1][s]) * (n-i+1);
 		//cout<<(dp[i][s]) * (n-i+1)<<endl;
 	}
 	cout<<ans<<endl;
    return 0;
}