#include<bits/stdc++.h>
using namespace std;
const int N = 3e3 + 5,MOD = 998244353;
#define int long long
int n,s;
int a[N],f[N];
int ans;
signed main() {
	scanf("%lld%lld",&n,&s);
	for(int i = 1;i <= n;++i)
		scanf("%lld",a+i);
	f[a[1]] = 1;
	for(int i = 2;i <= n;++i) {
		for(int j = s;j > a[i];--j)
			(f[j] += f[j-a[i]]) %= MOD;
		(f[a[i]] += i) %= MOD;
		(ans += f[s] % MOD) %= MOD;
	}
	printf("%lld\n",ans);
	return 0;
}


### Prompt

Create a solution in cpp for the following problem:

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<bits/stdc++.h>
using namespace std;
const int N = 3e3 + 5,MOD = 998244353;
#define int long long
int n,s;
int a[N],f[N];
int ans;
signed main() {
	scanf("%lld%lld",&n,&s);
	for(int i = 1;i <= n;++i)
		scanf("%lld",a+i);
	f[a[1]] = 1;
	for(int i = 2;i <= n;++i) {
		for(int j = s;j > a[i];--j)
			(f[j] += f[j-a[i]]) %= MOD;
		(f[a[i]] += i) %= MOD;
		(ans += f[s] % MOD) %= MOD;
	}
	printf("%lld\n",ans);
	return 0;
}


```