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>
using namespace std;

#define nax 100009
#define FOR(i,n,m) for(int i =(n);i<(m);i++)
#define REP(i,n) FOR(i,0,n)

typedef long long ll;
typedef vector<ll> vi;

int main(){
	ll dp[109][nax];
	ll n,k, mod = 1000000007LL;
	cin>>n>>k;
	vi a(n);
	REP(i,n) cin>>a[i];

	memset(dp,0LL,sizeof dp);
	REP(i,n) dp[i][0] = 1;
	REP(i,a[0]+1) dp[0][i] = 1;

	FOR(i,1,n){
		FOR(j,1,nax){
			dp[i][j] = (dp[i][j-1]%mod + dp[i-1][j]%mod)%mod;
			if(j-a[i]-1>=0) dp[i][j] = ((dp[i][j] - dp[i-1][j-a[i]-1])%mod+mod)%mod;
		}
	}

	cout<<dp[n-1][k]<<endl;

	return 0;
}