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

template<int MOD_> struct modnum {
    static constexpr int MOD = MOD_;
    static_assert(MOD_ > 0, "MOD must be positive");

private:
    using ll = long long;
    int v;
    static int minv(int a, int m) {
        a %= m;
        assert(a);
        return a == 1 ? 1 : int(m - ll(minv(m, a)) * ll(m) / a);
    }

public:
    modnum() : v(0) {}
    modnum(ll v_) : v(int(v_ % MOD)) {
        if (v < 0)
            v += MOD;
    }
    explicit operator int() const { return v; }
    friend ostream& operator<<(ostream& out, const modnum& n) {
        return out << int(n);
    }
    friend istream& operator>>(istream& in, modnum& n) {
        ll v_;
        in >> v_;
        n = modnum(v_);
        return in;
    }

    friend bool operator==(const modnum& a, const modnum& b) { return a.v == b.v; }
    friend bool operator!=(const modnum& a, const modnum& b) { return a.v != b.v; }

    modnum inv() const {
        modnum res;
        res.v = minv(v, MOD);
        return res;
    }
    friend modnum inv(const modnum& m) { return m.inv(); }
    modnum neg() const {
        modnum res;
        res.v = v ? MOD - v : 0;
        return res;
    }
    friend modnum neg(const modnum& m) { return m.neg(); }

    modnum operator-() const { return neg(); }
    modnum operator+() const { return modnum(*this); }
    modnum& operator++() {
        v++;
        if (v == MOD) v = 0;
        return *this;
    }
    modnum& operator--() {
        if (v == 0) v = MOD;
        v--;
        return *this;
    }
    modnum& operator+=(const modnum& o) {
        v += o.v;
        if (v >= MOD) v -= MOD;
        return *this;
    }
    modnum& operator-=(const modnum& o) {
        v -= o.v;
        if (v < 0) v += MOD;
        return *this;
    }
    modnum& operator*=(const modnum& o) { v = int(ll(v) * ll(o.v) % MOD); return *this; }
    modnum& operator/=(const modnum& o) { return *this *= o.inv(); }

    friend modnum operator++(modnum& a, int) { modnum r = a; ++a; return r; }
    friend modnum operator--(modnum& a, int) { modnum r = a; --a; return r; }
    friend modnum operator+(const modnum& a, const modnum& b) { return modnum(a) += b; }
    friend modnum operator-(const modnum& a, const modnum& b) { return modnum(a) -= b; }
    friend modnum operator*(const modnum& a, const modnum& b) { return modnum(a) *= b; }
    friend modnum operator/(const modnum& a, const modnum& b) { return modnum(a) /= b; }
};

using mint = modnum<(int)1e9 + 7>;

int main() {
    ios::sync_with_stdio(false), cin.tie(nullptr);
    int n, k;
    cin >> n >> k;
    vector<int> a(n);
    for (int& it : a) cin >> it;
    if (k == 0) {
        cout << "1\n";
        return 0;   
    }
    vector<mint> dp = {1};
    for (int x : a) {
        int y = dp.size();
        int i = 0, j = 0, lim = min(x + y, k + 2);
        vector<mint> nxt;   
        nxt.reserve(lim);
        for (int rep = 0; rep < lim; rep++) {
            nxt.push_back(dp[j] - (i ? dp[i - 1] : 0));
            if (j + 1 < y) j++;
            if (rep >= x) i++;
        }
        dp = nxt;
        for (int z = 1; z < (int)dp.size(); z++)
            dp[z] += dp[z - 1];
    }
    if (k >= (int)dp.size())
        cout << "0\n";
    else
        cout << dp[k] - dp[k - 1] << '\n';
    return 0;
}

Measured memory_bytes: 4304