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)

//Author:- S_Aditya

#include<bits/stdc++.h>
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
using namespace std;
//typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
#define ll long long 
#define scn(n) scanf("%d",&n)
#define lscn(n) scanf("%lld",&n)
#define lpri(n) printf("%lld",n)
#define pri(n) printf("%d",n)
#define pln() printf("\n")
#define priln(n) printf("%d\n",n)
#define lpriln(n) printf("%lld\n",n)
#define rep(i,init,n) for(int i=init;i<n;i++)
#define pb push_back     
#define mp make_pair
#define F first
#define S second
#define gcd __gcd
#define inf INT_MAX
#define ninf INT_MIN
const ll mod=1e9+7;         
const int N=1e5+4;

//dp[i][j] tells the no. of ways to distribute total of j candies among the first i boys
//according to the given constraints.

ll dp[104][N];

int main()                  
{
    int n,k;
    
    scn(n); scn(k);
    
    int a[n];
    
    rep(i,0,n)
    scn(a[i]);
    
    dp[0][0]=1;
    
    rep(i,0,n)
    {
        rep(j,1,k+1)
        dp[i][j]=(dp[i][j]+dp[i][j-1])%mod;
        
        rep(used,0,k+1)
        {
            int l=used,r=used+min(k-used,a[i]);
            
            dp[i+1][l]=(dp[i+1][l]+dp[i][used])%mod;
            
            dp[i+1][r+1]=(dp[i+1][r+1]-dp[i][used]+mod)%mod;
        }
    }
    
    cout<<dp[n][k];
}