Problem:
Score : 100 points

Problem Statement

There are N children, numbered 1, 2, \ldots, N.

They have decided to share K candies among themselves.
Here, for each i (1 \leq i \leq N), Child i must receive between 0 and a_i candies (inclusive).
Also, no candies should be left over.

Find the number of ways for them to share candies, modulo 10^9 + 7.
Here, two ways are said to be different when there exists a child who receives a different number of candies.

Constraints

All values in input are integers.

1 \leq N \leq 100

0 \leq K \leq 10^5

0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:

N K
a_1 a_2 \ldots a_N

Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Sample Input 1

3 4
1 2 3

Sample Output 1

5

There are five ways for the children to share candies, as follows:

(0, 1, 3)

(0, 2, 2)

(1, 0, 3)

(1, 1, 2)

(1, 2, 1)

Here, in each sequence, the i-th element represents the number of candies that Child i receives.

Sample Input 2

1 10
9

Sample Output 2

0

There may be no ways for the children to share candies.

Sample Input 3

2 0
0 0

Sample Output 3

1

There is one way for the children to share candies, as follows:

(0, 0)

Sample Input 4

4 100000
100000 100000 100000 100000

Sample Output 4

665683269

Be sure to print the answer modulo 10^9 + 7.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#include<vector>
#include<iostream>
#include<map>
#include<algorithm>
#include<cmath>
#include<queue>
#include<set>
#include<deque>
#define ll long long
using namespace std;
#define BUF_SIZE 1048576
char _buf[BUF_SIZE],*_is=_buf,*_it=_buf;
inline char rdc(){
	if (_is==_it) _it=(_is=_buf)+fread(_buf,1,BUF_SIZE,stdin);
	return *_is++;
}
inline int rdi(){
	int x=0,f=0;
	register char ch=rdc();
	while ((ch<'0' or ch>'9') and (ch^'-')) ch=rdc();
	if (ch=='-') f=1,ch=rdc();
	while (ch>='0' and ch<='9') x=(x<<3)+(x<<1)+(ch^'0'),ch=rdc();
	return f?-x:x;
}
inline void write(int x){
    if(x<0) putchar('-'),x=-x;
    if(x>9) write(x/10);
    putchar(x%10+'0');
}
inline void _write(int x){
	write(x);
	putchar(' ');
}
inline void print(int x){
	write(x);
	putchar('\n');
}
int n,k,x,sum;
int dp[105][100005];
const int md=1000000007;
int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	cin>>n>>k;
	int i,j;
	dp[0][0]=1;
	for(i=1;i<=n;++i){
		cin>>x;
		sum=0;
		for(j=0;j<=k;++j){
			sum+=dp[i-1][j];
			if(j>x) sum-=dp[i-1][j-x-1];
			if(sum>=md) sum-=md;
			if(sum<0) sum+=md;
			dp[i][j]=sum;
		}
	}
	cout<<dp[n][k]<<endl;
	return 0;
}