#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class T, class U> using Pa = pair<T, U>;
template <class T> using vec = vector<T>;
template <class T> using vvec = vector<vec<T>>;


constexpr ll mod = 998244353;
struct mint {
    ll x;
    mint(ll x=0):x((x%mod+mod)%mod){}
    
    friend ostream &operator<<(ostream& os,const mint& a){
        return os << a.x;
    }

    friend istream &operator>>(istream& is,mint& a){
        ll t;
        is >> t;
        a = mint(t);
        return (is);
    }

    mint& operator+=(const mint a) {
        if ((x += a.x) >= mod) x -= mod;
        return *this;
    }
    mint& operator-=(const mint a) {
        if ((x += mod-a.x) >= mod) x -= mod;
        return *this;
    }
    mint& operator*=(const mint a) {
        (x *= a.x) %= mod;
        return *this;
    }
    mint operator+(const mint a) const {
        mint res(*this);
        return res+=a;
    }
    mint operator-(const mint a) const {
        mint res(*this);
        return res-=a;
    }
    mint operator*(const mint a) const {
        mint res(*this);
        return res*=a;
    }
    mint pow(ll t) const {
        if (!t) return 1;
        mint a = pow(t>>1);
        a *= a;
        if (t&1) a *= *this;
        return a;
    }
    // for prime mod
    mint inv() const {
        return pow(mod-2);
    }
    mint& operator/=(const mint a) {
        return (*this) *= a.inv();
    }
    mint operator/(const mint a) const {
        mint res(*this);
        return res/=a;
    }
    bool operator==(const mint& r)const{
        return x==r.x;
    }
};


class combination{
public:
    vector<mint> fact,inv,finv;
    combination(int N){
        fact = inv = finv = vector<mint>(N+1);
        fact[0] = fact[1] = 1;
        inv[0] = inv[1] = 1;
        finv[0] = finv[1] = 1;
        for(ll i=2;i<=N;i++){
            fact[i] = fact[i-1]*i;
            inv[i] = (mint) mod - inv[mod%i]*(mod/i);
            finv[i] = finv[i-1]*inv[i];
        }
    }
    mint f(int i){
        return fact[i];
    }
    mint comb(int n,int k){
        if(n<k) return 0;
        if(n<0 || k<0) return 0;
        return fact[n]*finv[k]*finv[n-k];
    }
    mint hcomb(int n,int k){
        if(n==0 && k==0) return 1;
        return comb(n+k-1,k);
    }
};

namespace FastFourierTransform {
    using real = double;

    struct C {
        real x, y;

        C() : x(0), y(0) {}

        C(real x, real y) : x(x), y(y) {}

        inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }

        inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }

        inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }

        inline C conj() const { return C(x, -y); }
    };

    const real PI = acosl(-1);
    int base = 1;
    vector< C > rts = { {0, 0},
                        {1, 0} };
    vector< int > rev = {0, 1};


    void ensure_base(int nbase) {
        if(nbase <= base) return;
        rev.resize(1 << nbase);
        rts.resize(1 << nbase);
        for(int i = 0; i < (1 << nbase); i++) {
            rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
        }
        while(base < nbase) {
            real angle = PI * 2.0 / (1 << (base + 1));
            for(int i = 1 << (base - 1); i < (1 << base); i++) {
                rts[i << 1] = rts[i];
                real angle_i = angle * (2 * i + 1 - (1 << base));
                rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
            }
            ++base;
        }
    }

    void fft(vector< C > &a, int n) {
        assert((n & (n - 1)) == 0);
        int zeros = __builtin_ctz(n);
        ensure_base(zeros);
        int shift = base - zeros;
        for(int i = 0; i < n; i++) {
            if(i < (rev[i] >> shift)) {
                swap(a[i], a[rev[i] >> shift]);
            }
        }
        for(int k = 1; k < n; k <<= 1) {
            for(int i = 0; i < n; i += 2 * k) {
                for(int j = 0; j < k; j++) {
                    C z = a[i + j + k] * rts[j + k];
                    a[i + j + k] = a[i + j] - z;
                    a[i + j] = a[i + j] + z;
                }
            }
        }
    }

    vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {
        int need = (int) a.size() + (int) b.size() - 1;
        int nbase = 1;
        while((1 << nbase) < need) nbase++;
        ensure_base(nbase);
        int sz = 1 << nbase;
        vector< C > fa(sz);
        for(int i = 0; i < sz; i++) {
            int x = (i < (int) a.size() ? a[i] : 0);
            int y = (i < (int) b.size() ? b[i] : 0);
            fa[i] = C(x, y);
        }
        fft(fa, sz);
        C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
        for(int i = 0; i <= (sz >> 1); i++) {
            int j = (sz - i) & (sz - 1);
            C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
            fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
            fa[i] = z;
        }
        for(int i = 0; i < (sz >> 1); i++) {
            C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
            C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
            fa[i] = A0 + A1 * s;
        }
        fft(fa, sz >> 1);
        vector< int64_t > ret(need);
        for(int i = 0; i < need; i++) {
            ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
        }
        return ret;
    }
};

template< typename T >
struct ArbitraryModConvolution {
    using real = FastFourierTransform::real;
    using C = FastFourierTransform::C;

    ArbitraryModConvolution() = default;

    vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {
        if(need == -1) need = a.size() + b.size() - 1;
        int nbase = 0;
        while((1 << nbase) < need) nbase++;
        FastFourierTransform::ensure_base(nbase);
        int sz = 1 << nbase;
        vector< C > fa(sz);
        for(int i = 0; i < a.size(); i++) {
            fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);
        }
        fft(fa, sz);
        vector< C > fb(sz);
        if(a == b) {
            fb = fa;
        }else{
            for(int i = 0; i < b.size(); i++) {
                fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);
            }
            fft(fb, sz);
        }
        real ratio = 0.25 / sz;
        C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
        for(int i = 0; i <= (sz >> 1); i++) {
            int j = (sz - i) & (sz - 1);
            C a1 = (fa[i] + fa[j].conj());
            C a2 = (fa[i] - fa[j].conj()) * r2;
            C b1 = (fb[i] + fb[j].conj()) * r3;
            C b2 = (fb[i] - fb[j].conj()) * r4;
            if(i != j) {
                C c1 = (fa[j] + fa[i].conj());
                C c2 = (fa[j] - fa[i].conj()) * r2;
                C d1 = (fb[j] + fb[i].conj()) * r3;
                C d2 = (fb[j] - fb[i].conj()) * r4;
                fa[i] = c1 * d1 + c2 * d2 * r5;
                fb[i] = c1 * d2 + c2 * d1;
            }
            fa[j] = a1 * b1 + a2 * b2 * r5;
            fb[j] = a1 * b2 + a2 * b1;
        }
        fft(fa, sz);
        fft(fb, sz);
        vector< T > ret(need);
        for(int i = 0; i < need; i++) {
            int64_t aa = llround(fa[i].x);
            int64_t bb = llround(fb[i].x);
            int64_t cc = llround(fa[i].y);
            aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
            ret[i] = aa + (bb << 15) + (cc << 30);
        }
        return ret;
    }
};

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N,S;
    cin >> N >> S;
    vec<int> A(N);
    for(int i=0;i<N;i++) cin >> A[i];

    ArbitraryModConvolution<mint> NTT;

    auto make_vec = [](int x){
        vec<mint> v(x+1,0);
        v[0] = 2,v[x] = 1;
        return v;
    };

    auto rec = [&](auto&& self,int l,int r)->vec<mint>{
        if(r-l==1) return make_vec(A[l]);
        int m = (l+r)/2;
        auto res = NTT.multiply(self(self,l,m),self(self,m,r));
        res.resize(S+1);
        return res;
    };
    auto res = rec(rec,0,N);
    cout << res[S] << "\n";
}

Measured memory_bytes: 4860