#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)
#define rep2(i, x, n) for (int i = x; i <= n; i++)
#define rep3(i, x, n) for (int i = x; i >= n; i--)
#define each(e, v) for (auto &e : v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
// const int MOD = 1000000007;
const int MOD = 998244353;

template <int mod>
struct Mod_Int {
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    static int get_mod() { return mod; }

    Mod_Int &operator+=(const Mod_Int &p) {
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator-=(const Mod_Int &p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator*=(const Mod_Int &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    Mod_Int &operator/=(const Mod_Int &p) {
        *this *= p.inverse();
        return *this;
    }

    Mod_Int &operator++() { return *this += Mod_Int(1); }

    Mod_Int operator++(int) {
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int &operator--() { return *this -= Mod_Int(1); }

    Mod_Int operator--(int) {
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Mod_Int operator-() const { return Mod_Int(-x); }

    Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }

    Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }

    Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }

    Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }

    bool operator==(const Mod_Int &p) const { return x == p.x; }

    bool operator!=(const Mod_Int &p) const { return x != p.x; }

    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod - 2);
    }

    Mod_Int pow(long long k) const {
        Mod_Int now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }

    friend istream &operator>>(istream &is, Mod_Int &p) {
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};

using mint = Mod_Int<MOD>;

int main() {
    ll N, K;
    cin >> N >> K;

    vector<ll> a(N);
    rep(i, N) cin >> a[i];

    vector<ll> s = a;
    rep2(i, 1, N - 1) s[i] += s[i - 1];
    // print(s);

    int M = 20;
    vector<vector<mint>> dp(M, vector<mint>(2, 0)), ndp(M, vector<mint>(2, 0));
    dp[0][0] = 1;

    rep(i, N) {
        rep(j, M) rep(k, 2) ndp[j][k] = 0;
        rep(j, M) {
            rep(k, 2) {
                if (dp[j][k] == 0) continue;
                ll x = -INF;
                if (j > 0) x = (s[i - j] - 1) << (j - 1);
                // b[i] = a[i]
                {
                    int nj = (j == 0 ? 0 : j + 1), nk = k;
                    if (a[i] > x) nj = 0;
                    if (a[i] > 0) nk = 0;
                    if (nj < M) ndp[nj][nk] += dp[j][k];
                }
                // b[i] < a[i]
                {
                    if (x >= 0) {
                        if (a[i] - 1 > x) {
                            ll l = x + 1, r = a[i] - 1;
                            int nj = 1, nk = 0;
                            if (s[i] - 1 == 0) nk = 1;
                            ndp[nj][nk] += dp[j][k] * max(r - l + 1, 0LL);
                        }
                        if (x > 0) {
                            ll l = 1, r = min(x, a[i] - 1);
                            int nj = j + 1, nk = 0;
                            if (s[i] - 1 >= 2 * x) nj = 1;
                            if (s[i] - 1 == 0) nk = 1;
                            if (nj < M) ndp[nj][nk] += dp[j][k] * max(r - l + 1, 0LL);
                        }
                        {
                            ll l = -K, r = min(0LL, a[i] - 1);
                            int nj = j + 1, nk = k;
                            if (s[i] - 1 >= 2 * x) nj = 1;
                            if (s[i] - 1 == 0) nk = 1;
                            if (nj < M) ndp[nj][nk] += dp[j][k] * max(r - l + 1, 0LL);
                        }
                    } else {
                        if (a[i] - 1 > 0) {
                            ll l = 1, r = a[i] - 1;
                            int nj = 1, nk = 0;
                            if (s[i] - 1 == 0) nk = 1;
                            ndp[nj][nk] += dp[j][k] * max(r - l + 1, 0LL);
                        }
                        if (x < 0) {
                            ll l = max(-K, x + 1), r = min(0LL, a[i] - 1);
                            int nj = 1, nk = k;
                            if (s[i] - 1 == 0) nk = 1;
                            ndp[nj][nk] += dp[j][k] * max(r - l + 1, 0LL);
                        }
                        if (x >= -K) {
                            ll l = -K, r = min(x, a[i] - 1);
                            int nj = j + 1, nk = k;
                            if (s[i] - 1 >= 2 * x) nj = 1;
                            if (s[i] - 1 == 0) nk = 1;
                            if (nj < M) ndp[nj][nk] += dp[j][k] * max(r - l + 1, 0LL);
                        }
                    }
                }
            }
        }
        swap(dp, ndp);
        // cout << i << '\n';
        // rep(i, N) print(dp[i]);
    }

    cout << dp[0][0] << '\n';
}