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: Wrong Answer)

#include <bits/stdc++.h>
#include <stdio.h>
using namespace std;
 
#define int long long int
#define ld long double
#define mod 1000000007 
#define pii pair<int,int>
#define F first
#define S second
#define mp make_pair
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define forn(i,s, e) for (int i = s; i <= e; i++)
#define fornd(i,s, e) for (int i = s ; i >= e; i--)
#define autoit(x,it) for(auto it = x.begin(); it != x.end(); it++)
#define print(x) for(auto el: x) cout<<el<<" ";cout<<"\n"
#define PSET(x,y) fixed<<setprecision(y)<<x
// #define bits(x) __builtin_popcount(x)
#define fast ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
/*void fileio()
{
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
}*/
 
 
template <typename T> 
void swap(T& a, T& b){
    T temp = a;
    a = b;
    b = temp;
}
void selfadd(int& a, int b){
    a = a+b;
    if(a>=mod)
        a = a-mod;
}
void selfsub(int& a, int b){
    a = a-b+mod;
    if(a>=mod)
        a = a-mod;
}  
const int N = 100005; 
 
int dp[101][N];
vector<int> a;

void solve(){
    int n,k;
    cin>>n>>k;
    a.assign(n,0);
 
    forn(i,0,n-1)
        cin>>a[i];
 
    memset(dp,0,sizeof(dp));
    
    dp[0][0] = 1;

    for(int i=0;i<=a[0];i++)
        dp[0][i] = 1;

    for(int i=1;i<n;i++){
        int sum = 0;
        for(int j = 0;j<=k;j++){
            sum = dp[i-1][j];
            if(j>0)
                selfadd(sum, dp[i][j-1]);
            if(j>a[i]){
                selfsub(sum, dp[i-1][j-a[i]]);
            }            
            dp[i][j] = sum;
        }
    }
    cout<<dp[n-1][k];
}
 
int32_t main()
{
    //fileio();
    fast;
    // int t;
    // cin>>t;
    // for(int y=1;y<=t;y++)
    {
        // cout<<"Case #"<<y<<": ";
        solve();
    }
    return 0;
}