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 (Clang 3.8.0) (judge verdict: Accepted)

char buf[20000];sz;
inline int rd()
{
	int ret=0;
	for(;;)
	{
		char k=buf[sz++];
		if(k<'0')break;
		ret=ret*10+k-'0';
	}
	return ret;
}
int d[3001];
const int mod=998244353;
main()
{
	read(0,buf,20000);
	int N=rd();
	int S=rd();
	int ans=0;
	for(int i=0;i<N;i++)
	{
		++d[S];
		for(int j=rd(),k=0;j<=S;j++,k++)
		{
			d[k]+=d[j];
			d[k]-=mod*(d[k]>=mod);
		}
		ans+=d[0];
		if(ans>=mod)ans-=mod;
	}
	printf("%d",ans);
}