#include<iostream>
#include<cstring>
using namespace std;
int N=998244353;
int a[3005][3005],b[3005],n,s;
int main(){
	cin>>n>>s;
	for(int i=0;i<n;i++){
		cin>>b[i];
	}
	int sum=0;
	for(int i=0;i<n;i++){
		memcpy(a[i+1],a[i],sizeof(a[i]));
		a[i+1][b[i]]=(a[i+1][b[i]]+i+1)%N;
		for(int j=0;j<=s-b[i];j++){
			a[i+1][j+b[i]]=(a[i+1][j+b[i]]+a[i][j])%N;		
		}
		sum=(sum+a[i+1][s])%N;
	}
	cout<<sum;
	return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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.

Examples

Input

3 4
2 2 4


Output

5


Input

5 8
9 9 9 9 9


Output

0


Input

10 10
3 1 4 1 5 9 2 6 5 3


Output

152

### Response

```cpp
#include<iostream>
#include<cstring>
using namespace std;
int N=998244353;
int a[3005][3005],b[3005],n,s;
int main(){
	cin>>n>>s;
	for(int i=0;i<n;i++){
		cin>>b[i];
	}
	int sum=0;
	for(int i=0;i<n;i++){
		memcpy(a[i+1],a[i],sizeof(a[i]));
		a[i+1][b[i]]=(a[i+1][b[i]]+i+1)%N;
		for(int j=0;j<=s-b[i];j++){
			a[i+1][j+b[i]]=(a[i+1][j+b[i]]+a[i][j])%N;		
		}
		sum=(sum+a[i+1][s])%N;
	}
	cout<<sum;
	return 0;
}

```