#include <climits>
#include <queue>
#include <vector>
#include <map>
#include <cstdlib>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <sstream>  // istringstream buffer(myString);
#include <stack>
#include <algorithm>  //swap function is here
#include <cstring>
#include <cassert>
#include <bits/stdc++.h>
using namespace std;


#define bit(x,i) (x&(1<<i))  //select the bit of position i of x
#define lowbit(x) ((x)&((x)^((x)-1))) //get the lowest bit of x
#define hBit(msb,n) asm("bsrl %1,%0" : "=r"(msb) : "r"(n)) //get the highest bit of x, maybe the fastest
#define max(a,b) (a<b?b:a)
//__builtin_popcount(n);
#define IN(i,l,r) (l<i&&i<r) //the next for are for checking bound
#define LINR(i,l,r) (l<=i&&i<=r)
#define LIN(i,l,r) (l<=i&&i<r)
#define INR(i,l,r) (l<i&&i<=r)
#define F(i,L,R) for (int i = L; i < R; i++) //next four are for "for loops"
#define FE(i,L,R) for (int i = L; i <= R; i++)
#define FF(i,L,R) for (int i = L; i > R; i--)
#define FFE(i,L,R) for (int i = L; i >= R; i--)
#define getI(a) scanf("%d", &a) //next three are handy ways to get ints, it's also force you to use '&' sign
#define getII(a,b) scanf("%d%d", &a, &b)
#define getIII(a,b,c) scanf("%d%d%d", &a, &b, &c)
#define wez(n) int (n); scanf("%d",&(n)) //handy if the input is right after the definition of a variable
#define wez2(n,m) int (n),(m); scanf("%d %d",&(n),&(m))
#define wez3(n,m,k) int (n),(m),(k); scanf("%d %d %d",&(n),&(m),&(k))
#define TESTS wez(testow)while(testow--) //for multilple cases problems
#define whileZ int T; getI(T); while(T--) // the same as above
#define getS(x) scanf("%s", x) //get a char* string
#define clr(a,x) memset(a,x,sizeof(a)) //set elements of array to some value
#define char2Int(c) (c-'0')
#define lastEle(vec) vec[vec.size()-1]
#define SZ(x) ((int)((x).size()))
#define REMAX(a,b) (a)=max((a),(b)) // set a to the maximum of a and b
#define REMIN(a,b) (a)=min((a),(b));
#define FOREACH(i,t) for (typeof(t.begin()) i=t.begin(); i!=t.end(); i++) // traverse an STL data structure
#define ALL(c) (c).begin(),(c).end() //handy for function like "sort()"
#define PRESENT(c,x) ((c).find(x) != (c).end())
#define CPRESENT(c,x) (find(ALL(c),x) != (c).end())
#define ll long long //data types used often, but you don't want to type them time by time
#define ull unsigned long long
#define ui unsigned int
#define us unsigned short
#define IOS ios_base::sync_with_stdio(0); //to synchronize the input of cin and scanf
#define INF 1001001001
#define PI 3.1415926535897932384626
//for map, pair
#define mp make_pair
#define fi first
#define se second
// for debug
inline void pisz(int n) { printf("%d\n",n); }
#define DBG(vari) cerr<<#vari<<" = "<<(vari)<<endl;
#define printA(a,L,R) FE(i,L,R) cout << a[i] << (i==R?'\n':' ')
#define printV(a) printA(a,0,a.size()-1)
#define MAXN 10000
//for vectors
#define pb push_back
typedef int elem_t;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int,int> ii;
// directions
const int fx[4][2] = {{0,1}, {0,-1}, {1,0}, {-1,0}};
const int fxx[8][2] = {{0,1}, {0,-1}, {1,0}, {-1,0}, {1,1}, {1,-1}, {-1,1}, {-1,-1}};
template<typename T,typename TT> ostream& operator<<(ostream &s,pair<T,TT> t) {return s<<"("<<t.first<<","<<t.second<<")";}
template<typename T> ostream& operator<<(ostream &s,vector<T> t){F(i,0,SZ(t))s<<t[i]<<" ";return s; }
 
ll mod=1000000007;

ll gcd(ll a,ll b) 
{ 
    if (a == 0) 
        return b; 
    return gcd(b % a, a); 
} 

ll power(ll a,ll b,ll m)
{
    ll r=1;
    a=a%m;
    while(b)
    {
        if(b&1)r=r*a%m;
        a=a*a%m;
        b=b>>1;
    }
return r;
}


ll dp[101][100001];

int main()
{


ios::sync_with_stdio(false);
 cin.tie(0);
 cout.tie(0);

 ll n;
 cin>>n;

 ll k;
 cin>>k;

 ll arr[n];

 for (int i = 0; i < n; ++i)
 {
    cin >> arr[i];
     /* code */
 }
 //cout<<"YES\n";
 // intital state

 // ways of having atleast j candies remaining after considering ith kid
 for (int i = 0; i <= k; ++i)
 {
    if(i!=0)
       dp[0][i] = dp[0][i-1];

    if(k-i<=arr[0] && i<=k)
    {
        dp[0][i]++;
    }
    dp[0][i] = dp[0][i]%mod;
    /* code */
 }

 for (int i = 1; i <= n ; ++i)
 {
    for (int j = 0; j <= k; ++j)
    {
        if(j==0)
        {

         dp[i][j] =  dp[i-1][min(k,j+arr[i])]%mod;

        }
        else
        dp[i][j] = (dp[i][j-1] + dp[i-1][min(k,j+arr[i])]-dp[i-1][j-1]);

        dp[i][j] = dp[i][j]%mod;
        /* code */
    }
     /* code */
 }

if(dp[n-1][0]<0)
cout << dp[n-1][0]+mod <<"\n";
else
cout << dp[n-1][0] <<"\n";




}

Measured memory_bytes: 79104