#include <bits/stdc++.h>

#include <ext/pb_ds/assoc_container.hpp> // Common file
#include <ext/pb_ds/tree_policy.hpp>

using namespace __gnu_pbds;
using namespace std;

using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vb = vector<bool>;
using vd = vector<double>;
using vs = vector<string>;

typedef tree<
ll,
null_type,
less<ll>,
rb_tree_tag,
tree_order_statistics_node_update>
ordered_set;
// ordered_set X;
// *X.find_by_order(i) = ith largest element (counting from zero)
// X.order_of_key(k) = number of items in X < k (strict lt)

template<int MOD> struct modnum {
    int v;
    modnum() : v(0) {}
    modnum(ll _v) : v(_v % MOD) { if (v < 0) v += MOD; }
    explicit operator int() const { return v; }
    friend istream& operator >> (istream& i, modnum& n) { ll w; i >> w; n = modnum(w); return i; }
    friend ostream& operator << (ostream& o, const modnum& n) { return o << n.v; }

    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& 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 - () { modnum res; if (v) res.v = MOD - v; return res; }
    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; }

    modnum pow(ll e) const {
        if (e < 0) return 1 / this->pow(-e);
        if (e == 0) return 1;
        if (e & 1) return *this * this->pow(e-1);
        return (*this * *this).pow(e/2);
    }

    modnum inv() const {
        int g = MOD, x = 0, y = 1;
        for (int r = v; r != 0; ) {
            int q = g / r;
            g %= r; swap(g, r);
            x -= q * y; swap(x, y);
        }

        assert(g == 1);
        assert(y == MOD || y == -MOD);
        return x < 0 ? x + MOD : x;
    }
    modnum& operator /= (const modnum& o) { return (*this) *= o.inv(); }
    friend modnum operator / (const modnum& a, const modnum& b) { return modnum(a) /= modnum(b); }

    static int totient() {
        int tot = MOD, tmp = MOD;
        for (int p = 2; p * p <= tmp; p++) if (tmp % p == 0) {
            tot = tot / p * (p - 1);
            while (tmp % p == 0) tmp /= p;
        }
        if (tmp > 1) tot = tot / tmp * (tmp - 1);
        return tot;
    }

    static int primitive_root() {
        if (MOD == 1) return 0;
        if (MOD == 2) return 1;

        int tot = totient(), tmp = tot;
        vi tot_pr;
        for (int p = 2; p * p <= tmp; p++) if (tot % p == 0) {
            tot_pr.push_back(p);
            while (tmp % p == 0) tmp /= p;
        }
        if (tmp > 1) tot_pr.push_back(tmp);

        for (int r = 2; r < MOD; r++) if (__gcd(r, MOD) == 1) {
            bool root = true;
            for (int p : tot_pr) root &= modnum(r).pow(tot / p) != 1;
            if (root) return r;
        }
        assert(false);
    }

    static modnum generator() { static modnum g = primitive_root(); return g; }
    static int discrete_log(modnum v) {
        static const int M = ceil(sqrt(MOD));
        static unordered_map<int, int> table;
        if (table.empty()) {
            modnum e = 1;
            for (int i = 0; i < M; i++) { table[e.v] = i; e *= generator(); }
        }
        static modnum f = generator().pow(totient() - M);

        for (int i = 0; i < M; i++) {
            if (table.count(v.v)) return table[v.v] + i * M;
            v *= f;
        }
        assert(false);
    }

    static modnum unity_root(int deg) {
        assert(totient() % deg == 0);
        return generator().pow(totient() / deg);
    }

    static modnum fact(int n) {
        static vector<modnum> fact = { 1 };
        for (assert(n >= 0); fact.size() <= n; )
            fact.push_back(fact.back() * fact.size());
        return fact[n];
    }

    static modnum finv(int n) {
        static vector<modnum> finv = { 1 };
        for (assert(n >= 0); finv.size() <= n; )
            finv.push_back(finv.back() / finv.size());
        return finv[n];
    }

    static modnum ncr(int n, int r) {
        assert(n >= 0);
        if (r < 0 || n < r) return 0;
        return fact(n) * finv(r) * finv(n - r);
    }
};

constexpr ll MOD = 998244353;

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    
    int N, M;
    cin >> N >> M;

    int X = max(N, 2*M);
    vector<modnum<MOD>> spreads(X+1, 0);
    spreads[0] = 1;
    for(int x=1;x<=X;x++) spreads[x] = spreads[x-1] + modnum<MOD>::ncr(x+N-2, N-2);

    // cout << spreads[0] << " " << spreads[1] << " " << spreads[2] << endl;

    modnum<MOD> total = 0;
    for(int k = (M%2); k<=min(N, M); k+=2){
        int r = (3*M - k)/2;
        modnum<MOD> term = modnum<MOD>::ncr(N+r-1, N-1);
        // cout << k << " " << r << " " << r-M << " " << r-M-1 << " " << term << endl;
        if (r>=M) term -= k*spreads[r-M];
        if (r>=M+1) term -= (N-k)*spreads[r-M-1];
        // cout << term << endl;
        total += modnum<MOD>::ncr(N, k) * term;
    }

    cout << total << endl;
/*
    modnum<MOD> bad = 0;
    for (int x=2*M+1; x<=3*M;x++) {
        bad += modnum<MOD>::ncr(3*M - x + N - 2, N - 2);
    }

    modnum<MOD> ans = total - N * bad;
    cout << ans << endl;*/


    return 0;
}

Measured memory_bytes: 18668