#include <bits/stdc++.h>
using namespace std;

#define NDEBUG
#ifdef DEBUG
#include "../cout11.h"
#undef NDEBUG
#endif
#include <cassert>

#ifdef DEBUG
#define debug(fmt, ...) fprintf(stderr, fmt, __VA_ARGS__)
#else
#define debug(fmt, ...)
#endif

typedef long long ll;
typedef long double Double;
typedef unsigned long long ull;
typedef pair<int,int> ii;
typedef pair<ll,ll> llll;
typedef pair<double,double> dd;

typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<ii> vii;
typedef vector<vector<ii>> vvii;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<llll> vllll;
typedef vector<bool> vb;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<long double> vD;

#define sz(a)  int((a).size())
#define pb  push_back
#define eb  emplace_back
#define FOR(var,from,to) for(int var=(from);var<=(to);++var)
#define rep(var,n)  for(int var=0;var<(n);++var)
#define rep1(var,n)  for(int var=1;var<=(n);++var)
#define repC2(vari,varj,n)  for(int vari=0;vari<(n)-1;++vari)for(int varj=vari+1;varj<(n);++varj)
#define repC3(vari,varj,vark,n)  for(int vari=0;vari<(n)-2;++vari)for(int varj=vari+1;varj<(n)-1;++varj)for(int vark=varj+1;vark<(n);++vark)
#define ALL(c)  (c).begin(),(c).end()
#define RALL(c)  (c).rbegin(),(c).rend()
#define tr(i,c)  for(auto i=(c).begin(); i!=(c).end(); ++i)
#define found(s,e)  ((s).find(e)!=(s).end())
#define mset(arr,val)  memset(arr,val,sizeof(arr))
#define mid(x,y) ((x)+((y)-(x))/2)
#define IN(x,a,b) ((a)<=(x)&&(x)<=(b))
#define cons make_pair

template<class T> inline void amin(T & a, T const & b) { a = min(a, b); }
template<class T> inline void amax(T & a, T const & b) { a = max(a, b); }
template<typename X, typename T> auto vectors(X x, T a) { return vector<T>(x, a); }
template<typename X, typename Y, typename Z, typename... Zs> auto vectors(X x, Y y, Z z, Zs... zs) { auto cont = vectors(y, z, zs...); return vector<decltype(cont)>(x, cont); }



ll gcd(ll a, ll b) { while(a) swap(a, b%=a); return b; }

const ll MOD=1000000007LL;

ll ADD(ll x, ll y) { return (x+y) % MOD; }
ll SUB(ll x, ll y) { return (x-y+MOD) % MOD; }
ll MUL(ll x, ll y) { return x*y % MOD; }
ll POW(ll x, ll e) { ll v=1; for(; e; x=MUL(x,x), e>>=1) if (e&1) v = MUL(v,x); return v; }
ll DIV(ll x, ll y) { /*assert(y%MOD!=0);*/ return MUL(x, POW(y, MOD-2)); }
// ll comb(ll n, ll k) { ll v=1; for(ll i=1; i<=k; i++) v = DIV(MUL(v, n-i+1),i); return v; }
//

#define INTSPACE 12
char _buf[INTSPACE*1000000 + 3];

int loadint() {
    if (fgets(_buf, INTSPACE+3, stdin)==NULL) return 0;
    return atoi(_buf);
}

int loadvec(vector<int>& v, int N=-1) {
    if (N == 0) {
        v.clear();
        return 0;
    }
    if (N == -1) {
        N = loadint();
        if (N==0) return 0;
    }
    int bufsize = INTSPACE*N + 3;
    if (fgets(_buf, bufsize, stdin)==NULL) return 0;
    v.resize(N);

    int i=0;
    bool last = false;
    for (char *p=&_buf[0]; ;) {
        char *q = p;
        while (*q > ' ') ++q;
        if (*q == 0x0D || *q == 0x0A) last = true;
        *q = 0;
        v[i++] = atoi(p);
        if (last || i == N) break;
        p = q+1;
    }
    // assert(i <= N);
    return i;
}
void read_cr() {
    fgets(_buf, 256, stdin);
}

ll solve(int N, int K, vi& a) {
    int W = K*2+1;

    vll x(1, 0), y, ac;
    x[0] = 1;
#ifdef DEBUG
    // cerr << x << endl;
#endif

    rep(i,N){ // 1e2
        int X = x.size();
        ac.resize(X+1);
        ac[0]=0; rep(j,X) { ac[j+1] = (ac[j] + x[j])%MOD;} // 1e5

        int ai = a[i], A=ai+1;// 0 .. ai
        y.resize(X+ai);
        rep(j,X+ai) {
            int to = min(X-1, j)+1, fr = 0; // (0,j) -> (j,0)
            if (j > ai) fr += (j-ai);
            y[j] = SUB(ac[to], ac[fr]);
        }

#ifdef DEBUG
        cerr << y << endl;
#endif
        swap(y, x);
        x.resize(K+1);
    }
    return x[K];
}

int main() {
    int N,K; scanf("%d%d",&N,&K); read_cr();
    vi a(N);
    loadvec(a, N);
    cout << solve(N,K,a) << endl;
    return 0;
}


Measured memory_bytes: 5428