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;
typedef long long ll;
typedef long double ld;
template <typename X> ostream& operator << (ostream& x,const vector<X>& v){for(ll i=0;i<v.size();++i) x<<v[i]<<" ";return x;}
template <typename X> ostream& operator << (ostream& x,const set<X>& v){for(auto it:v) x<<it<<" ";return x;}
template <typename X, typename Y> ostream& operator << (ostream& x, const pair<X,Y>& v) {x<<v.ff<<" "<<v.ss;return x;}
template <typename T, typename S> ostream& operator << (ostream& os, const map<T, S>& v) { for (auto it : v) os << it.first << "=>" << it.second << endl; return os; }
struct pair_hash {inline std::size_t operator()(const std::pair<ll, ll> & v) const {return v.first*31+v.second;}};
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize ("O3")
#pragma GCC optimize ("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define speed ios_base::sync_with_stdio(false);cin.tie(NULL)
#define pb push_back
#define fr first
#define sc second
#define prnt(m) for(auto it = m.begin() ; it != m.end() ; ++it){cout<<*it<<endl;}
#define tra(it,m) for(auto it=m.begin();it!=m.end();++it)
#define DBG(x) cout<<"# # #     "<<x<<'\n';
#define fri(i,s,n) for(long long i=s;i<n;i++)
#define mod 1000000007LL
#define mod2 998244353
#define vct2 vector<vector<ll>>
#define vct vector<ll>
#define pll pair<ll,ll>
#define rz(n) resize(n)
#define all(v) v.begin(),v.end()
#define mkp make_pair
#define arrin(a,n) for(ll i = 0; i < n ; i++){cin>>a[i];}
#define arrout(a,n) for(ll i = 0;i < n; i++){cout<<a[i]<<" ";}
#define ex(s) cout<<s<<endl,exit(0);
#define infy 2e18
#define five 100005;
#define six 1000005;
#define printclock cerr<<"Time : "<<1000*(ld)clock()/(ld)CLOCKS_PER_SEC<<"ms\n";
//___________________________________________________________________________________________________________________________________________________________
const int N = five;
ll dp[N];
ll pre[N];
int main()
{
       int n,k;
       cin>>n>>k;
       int a[n];
       arrin(a,n);
       memset(dp,0,sizeof dp);
       memset(pre,0,sizeof pre);
       fri(i,0,a[0]+1){dp[i] = 1;}
       fri(i,1,n)
       {
              pre[0] = dp[0];
              fri(j,1,k+1)
              {
                     pre[j] = pre[j-1]+dp[j];
                     pre[j] %= mod;
              }
              for(ll j = k ; j >= 1 ; j--)
              {
                     ll add = 0;
                     dp[j] = pre[j];
                     if(j>a[i])dp[j] += (mod-pre[j-a[i]-1]);
                     dp[j] %= mod;
                     //cout<<j<<" "<<dp[j]<<endl;
              }
       }
       cout<<dp[k]<<endl;
}