// #pragma GCC target("avx") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") #include using namespace std; #define rep(i,n) for(int i = 0; i < (int)n; i++) #define FOR(n) for(int i = 0; i < (int)n; i++) #define repi(i,a,b) for(int i = (int)a; i < (int)b; i++) #define all(x) x.begin(),x.end() //#define mp make_pair #define vi vector #define vvi vector #define vvvi vector #define vvvvi vector #define pii pair #define vpii vector> template void chmax(T &a, const T &b) {a = (a > b? a : b);} template void chmin(T &a, const T &b) {a = (a < b? a : b);} using ll = long long; using ld = long double; using ull = unsigned long long; const ll INF = numeric_limits::max() / 2; const ld pi = 3.1415926535897932384626433832795028; const ll mod = 998244353; int dx[] = {1, 0, -1, 0, -1, -1, 1, 1}; int dy[] = {0, 1, 0, -1, -1, 1, -1, 1}; #define int long long template struct Modular_Int { long long x; Modular_Int() = default; Modular_Int(long long x_) : x(x_ >= 0? x_%MOD : (MOD-(-x_)%MOD)%MOD) {} long long val() const { return (x%MOD+MOD)%MOD; } long long get_mod() const { return MOD; } Modular_Int& operator^=(long long d) { Modular_Int ret(1); long long nx = x; while(d) { if(d&1) ret *= nx; (nx *= nx) %= MOD; d >>= 1; } *this = ret; return *this; } Modular_Int operator^(long long d) const {return Modular_Int(*this) ^= d;} Modular_Int pow(long long d) const {return Modular_Int(*this) ^= d;} //use this basically Modular_Int inv() const { return Modular_Int(*this) ^ (MOD-2); } //only if the module number is not prime //Don't use. This is broken. // Modular_Int inv() const { // long long a = (x%MOD+MOD)%MOD, b = MOD, u = 1, v = 0; // while(b) { // long long t = a/b; // a -= t*b, swap(a, b); // u -= t*v, swap(u, v); // } // return Modular_Int(u); // } Modular_Int& operator+=(const Modular_Int other) { if((x += other.x) >= MOD) x -= MOD; return *this; } Modular_Int& operator-=(const Modular_Int other) { if((x -= other.x) < 0) x += MOD; return *this; } Modular_Int& operator*=(const Modular_Int other) { long long z = x; z *= other.x; z %= MOD; x = z; if(x < 0) x += MOD; return *this; } Modular_Int& operator/=(const Modular_Int other) { return *this = *this * other.inv(); } Modular_Int& operator++() { x++; if (x == MOD) x = 0; return *this; } Modular_Int& operator--() { if (x == 0) x = MOD; x--; return *this; } Modular_Int operator+(const Modular_Int other) const {return Modular_Int(*this) += other;} Modular_Int operator-(const Modular_Int other) const {return Modular_Int(*this) -= other;} Modular_Int operator*(const Modular_Int other) const {return Modular_Int(*this) *= other;} Modular_Int operator/(const Modular_Int other) const {return Modular_Int(*this) /= other;} Modular_Int& operator+=(const long long other) {Modular_Int other_(other); *this += other_; return *this;} Modular_Int& operator-=(const long long other) {Modular_Int other_(other); *this -= other_; return *this;} Modular_Int& operator*=(const long long other) {Modular_Int other_(other); *this *= other_; return *this;} Modular_Int& operator/=(const long long other) {Modular_Int other_(other); *this /= other_; return *this;} Modular_Int operator+(const long long other) const {return Modular_Int(*this) += other;} Modular_Int operator-(const long long other) const {return Modular_Int(*this) -= other;} Modular_Int operator*(const long long other) const {return Modular_Int(*this) *= other;} Modular_Int operator/(const long long other) const {return Modular_Int(*this) /= other;} bool operator==(const Modular_Int other) const {return (*this).val() == other.val();} bool operator!=(const Modular_Int other) const {return (*this).val() != other.val();} bool operator==(const long long other) const {return (*this).val() == other;} bool operator!=(const long long other) const {return (*this).val() != other;} Modular_Int operator-() const {return Modular_Int(0LL)-Modular_Int(*this);} // friend constexpr istream& operator>>(istream& is, mint& x) noexcept { // long long X; // is >> X; // x = X; // return is; // } // friend constexpr ostream& operator<<(ostream& os, mint& x) { // os << x.val(); // return os; // } }; // const long long MOD_VAL = 1e9+7; const long long MOD_VAL = 998244353; using mint = Modular_Int; vector f = {1}, rf = {1}; void factor_init(long long n) { ++n; f.resize(n, 0); rf.resize(n, 0); f[0] = 1; repi(i, 1, n) f[i] = (f[i - 1] * i); rf[n-1] = f[n-1].inv(); for(int i = n-1; i > 0; --i) rf[i-1] = rf[i] * i; } mint P(long long n, long long k) { if(n= K, "; cerr << "where n=" << n << ",k=" << k << "\n\n"; return 0; } while(n > f.size()-1) { f.push_back(f.back() * f.size()); rf.push_back(f.back().inv()); } return f[n] * f[n-k]; } mint C(long long n, long long k) { if(n= K, "; cerr << "where n=" << n << ",k=" << k << "\n\n"; return 0; } while(n > f.size()-1) { f.push_back(f.back() * f.size()); rf.push_back(f.back().inv()); } return f[n]*rf[n-k]*rf[k]; } mint H(long long n, long long k) { assert(n>=1); return C(n+k-1, k); } mint Cat(long long n) { return C(2*n, n)-C(2*n, n-1); } void solve() { int n, k; cin >> n >> k; vi c(n), d(n); FOR(n) cin >> c[i]; FOR(n) cin >> d[i]; vector order(n); iota(all(order), 0); sort(all(order), [&](int i, int j) { if(c[i] != c[j]) return c[i] < c[j]; return d[i] > d[j]; }); vector duplicate; { vi nc, nd; for(int i : order) { nc.push_back(c[i]); nd.push_back(d[i]); } c = nc, d = nd; nc.clear(); nd.clear(); nc.push_back(c[0]); nd.push_back(d[0]); duplicate.push_back(1); FOR(n-1) { if(c[i] != c[i+1]) { nc.push_back(c[i+1]); nd.push_back(d[i+1]); duplicate.push_back(1); }else if(d[i] == d[i+1]) { duplicate.back() += 1; } } c = nc; d = nd; n = (int)c.size(); } //dp[i][j] = i番目までで満腹度がjであって食べた料理の個数がk個であるときの // first: 幸福度の最大値, second: 通り数 vector> coeff(n, vector(1001)); rep(i, n) { coeff[i][0] = 1; rep(j, 1000) { coeff[i][j+1] = coeff[i][j] * duplicate[i]; } } vector>>> dp(2, vector>>(k+1, vector>(k+1, make_pair(0, 0)))); dp[0][0][0] = make_pair(0, 1); rep(i, n) { int now = i&1; int nxt = 1^now; dp[nxt] = dp[now]; for(int j = 1; j*c[i] <= k; ++j) { for(int l = 0; l <= k-j*c[i]; ++l) { for(int m = 0; m <= k-j; ++m) if(dp[now][l][m].second != 0) { int happiness = dp[now][l][m].first + j*d[i]; if(dp[nxt][l+j*c[i]][m+j].first < happiness) { dp[nxt][l+j*c[i]][m+j].first = happiness; dp[nxt][l+j*c[i]][m+j].second = dp[now][l][m].second * H(m+1, j) * coeff[i][j]; }else if(dp[nxt][l+j*c[i]][m+j].first == happiness) { dp[nxt][l+j*c[i]][m+j].second += dp[now][l][m].second * H(m+1, j) * coeff[i][j]; } } } } } int bit_id = n&1; int mx = 0; mint ans = 0; rep(i, k+1) rep(j, k+1) { if(mx < dp[bit_id][i][j].first) { mx = dp[bit_id][i][j].first; ans = dp[bit_id][i][j].second; }else if(mx == dp[bit_id][i][j].first) { ans += dp[bit_id][i][j].second; } } cout << mx << endl; cout << ans.val() << endl; // for(auto e : c) cout << e << " "; cout << "\n"; // for(auto e : d) cout << e << " "; cout << "\n"; } signed main() { cin.tie(nullptr); ios::sync_with_stdio(false); solve(); return 0; }