結果

問題 No.2004 Incremental Coins
ユーザー heno239
提出日時 2023-04-29 18:49:44
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,574 ms / 2,000 ms
コード長 10,530 bytes
コンパイル時間 2,646 ms
コンパイル使用メモリ 183,240 KB
最終ジャッジ日時 2025-02-12 16:07:14
ジャッジサーバーID
（参考情報） 		judge4 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 20
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;
//#define int long long
typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 998244353;
//constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
template<typename T>
void chmin(T& a, T b) {
    a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
    a = max(a, b);
}
template<typename T>
void cinarray(vector<T>& v) {
    rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
    rep(i, v.size()) {
        if (i > 0)cout << " "; cout << v[i];
    }
    cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
    if (n < 0) {
        ll res = mod_pow(x, -n, m);
        return mod_pow(res, m - 2, m);
    }
    if (abs(x) >= m)x %= m;
    if (x < 0)x += m;
    //if (x == 0)return 0;
    ll res = 1;
    while (n) {
        if (n & 1)res = res * x % m;
        x = x * x % m; n >>= 1;
    }
    return res;
}
struct modint {
    int n;
    modint() :n(0) { ; }
    modint(ll m) {
        if (m < 0 || mod <= m) {
            m %= mod; if (m < 0)m += mod;
        }
        n = m;
    }
    operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
    if (n == 0)return modint(1);
    modint res = (a * a) ^ (n / 2);
    if (n % 2)res = res * a;
    return res;
}
ll inv(ll a, ll p) {
    return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
    fact[0] = modint(1);
    for (int i = 0; i < max_n - 1; i++) {
        fact[i + 1] = fact[i] * modint(i + 1);
    }
    factinv[max_n - 1] = modint(1) / fact[max_n - 1];
    for (int i = max_n - 2; i >= 0; i--) {
        factinv[i] = factinv[i + 1] * modint(i + 1);
    }
}
modint comb(int a, int b) {
    if (a < 0 || b < 0 || a < b)return 0;
    return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
    if (a < 0 || b < 0 || a < b)return 0;
    return fact[a] * factinv[a - b];
}
ll gcd(ll a, ll b) {
    a = abs(a); b = abs(b);
    if (a < b)swap(a, b);
    while (b) {
        ll r = a % b; a = b; b = r;
    }
    return a;
}
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
    if (loc >= v.size())v.resize(loc + 1, 0);
    v[loc] += val;
}
/*const int mn = 100005;
bool isp[mn];
vector<int> ps;
void init() {
    fill(isp + 2, isp + mn, true);
    for (int i = 2; i < mn; i++) {
        if (!isp[i])continue;
        ps.push_back(i);
        for (int j = 2 * i; j < mn; j += i) {
            isp[j] = false;
        }
    }
}*/
//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
    auto res = st.lower_bound(val);
    if (res == st.begin())return st.end();
    res--; return res;
}
//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
    auto res = st.lower_bound(val);
    return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
    return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
    a = a + b; return a;
}
mP operator-(mP a, mP b) {
    return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
    a = a - b; return a;
}
mt19937 mt(time(0));
const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------
int get_premitive_root() {
    int primitive_root = 0;
    if (!primitive_root) {
        primitive_root = [&]() {
            set<int> fac;
            int v = mod - 1;
            for (ll i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;
            if (v > 1) fac.insert(v);
            for (int g = 1; g < mod; g++) {
                bool ok = true;
                for (auto i : fac) if (mod_pow(g, (mod - 1) / i) == 1) { ok = false; break; }
                if (ok) return g;
            }
            return -1;
        }();
    }
    return primitive_root;
}
const int proot = get_premitive_root();
int bsf(int x) {
    int res = 0;
    while (!(x & 1)) {
        res++; x >>= 1;
    }
    return res;
}
int ceil_pow2(int n) {
    int x = 0;
    while ((1 << x) < n) x++;
    return x;
}
using poly = vector<modint>;
void butterfly(poly& a) {
    int n = int(a.size());
    int g = proot;
    int h = ceil_pow2(n);
    static bool first = true;
    static modint sum_e[30];  // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
    if (first) {
        first = false;
        modint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mod - 1);
        modint e = mod_pow(g, (mod - 1) >> cnt2);
        modint ie = (modint)1 / e;
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        modint now = 1;
        for (int i = 0; i < cnt2 - 2; i++) {
            sum_e[i] = es[i] * now;
            now *= ies[i];
        }
    }
    for (int ph = 1; ph <= h; ph++) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        modint now = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p] * now;
                a[i + offset] = l + r;
                a[i + offset + p] = l - r;
            }
            now *= sum_e[bsf(~(unsigned int)(s))];
        }
    }
}
void butterfly_inv(poly& a) {
    int n = int(a.size());
    int g = proot;
    int h = ceil_pow2(n);
    static bool first = true;
    static modint sum_ie[30];  // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
    if (first) {
        first = false;
        modint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mod - 1);
        modint e = mod_pow(g, (mod - 1) >> cnt2);
        modint ie = (modint)1 / e;
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        modint now = 1;
        for (int i = 0; i < cnt2 - 2; i++) {
            sum_ie[i] = ies[i] * now;
            now *= es[i];
        }
    }
    for (int ph = h; ph >= 1; ph--) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        modint inow = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p];
                a[i + offset] = l + r;
                a[i + offset + p] =
                    (unsigned long long)(mod + (ll)l - (ll)r) *
                    (ll)inow;
            }
            inow *= sum_ie[bsf(~(unsigned int)(s))];
        }
    }
}
poly multiply(poly g, poly h) {
    int n = g.size();
    int m = h.size();
    if (n == 0 || m == 0)return {};
    if (min(g.size(), h.size()) < 60) {
        poly res(g.size() + h.size() - 1);
        rep(i, g.size())rep(j, h.size()) {
            res[i + j] += g[i] * h[j];
        }
        return res;
    }
    int z = 1 << ceil_pow2(n + m - 1);
    g.resize(z);
    butterfly(g);
    h.resize(z);
    butterfly(h);
    rep(i, z) {
        g[i] *= h[i];
    }
    butterfly_inv(g);
    g.resize(n + m - 1);
    modint iz = (modint)1 / (modint)z;
    rep(i, n + m - 1) {
        g[i] *= iz;
    }
    return g;
}
const int mn = 1 << 18;
vector<int> G[mn];
vector<int> par;
queue<vector<int>> q;
bool exi[mn];
modint a[mn];
modint c[mn];
modint ans[mn];
void yaru(vector<int> v) {
    if (v.empty())return;
    //coutarray(v);
    //初期化
    for (int id : v)exi[id] = true;
    int g; int sz = v.size();
    function<int(int, int)> s_root = [&](int id, int fr)->int {
        int res = 1;
        int ma = 0;
        for (int to : G[id]) {
            if (to == fr)continue;
            if (!exi[to])continue;
            int nex = s_root(to, id);
            ma = max(ma, nex);
            res += nex;
        }
        if (ma <= sz / 2 && sz - res <= sz / 2)g = id;
        return res;
    };
    s_root(v[0], -1);
    //ここまで初期化
    //cout << "hello\n";
    vector<modint> bb;
    ans[g] += a[g];
    addv(bb, 0, a[g]);
    //重心を根としてなんかやる
    function<void(int, int)> dfs = [&](int id, int dep) {
        if (!exi[id])return;
        addv(bb, dep, a[id]);
        ans[g] += c[dep] * a[id];
        for (int to : G[id]) {
            dfs(to, dep + 1);
        }
    };
    for (int to : G[g])dfs(to, 1);
    reverse(all(bb));
    vector<int> ps;
    int cur = par[g];
    while (cur >= 0 && exi[cur]) {
        ps.push_back(cur);
        cur = par[cur];
    }
    vector<modint> cc(ps.size() + bb.size() + 1);
    rep(i, cc.size())cc[i] = c[i];
    vector<modint> bc = multiply(bb, cc);
    rep(i, ps.size()) {
        int loc = i + bb.size();
        if (loc < bc.size()) {
            ans[ps[i]] += bc[loc];
        }
    }
    //ここまで
    set<int> ban;
    ban.insert(g);
    vector<vector<int>> chs;
    vector<int> nexs;
    function<void(int, int)> search_next = [&](int id, int fr) {
        if (!exi[id])return;
        ban.insert(id);
        nexs.push_back(id);
        for (int to : G[id]) {
            if (to == fr)continue;
            search_next(to, id);
        }
    };
    //子を列挙する
    for (int to : G[g]) {
        search_next(to, g);
        if (nexs.empty())continue;
        q.push(nexs);
        chs.push_back(nexs);
        nexs.clear();
    }
    vector<int> nv;
    for (int id : v)if (!ban.count(id))nv.push_back(id);
    if (nv.size()) {
        q.push(nv);
    }
    //子達についてなんかやる
    for (int id : v)exi[id] = false;
}
void uoo(int n) {
    vector<int> ori(n); rep(i, n)ori[i] = i;
    q.push(ori);
    while (!q.empty()) {
        vector<int> v = q.front(); q.pop();
        yaru(v);
    }
}
void solve() {
    int n; ll k; cin >> n >> k;
    rep(i, n + 1) {
        ll x; cin >> x; a[i] = x;
    }
    par.resize(n + 1);
    par[0] = -1;
    rep1(i, n) {
        int p; cin >> p;
        par[i] = p;
        G[p].push_back(i);
    }
    c[0] = 1;
    modint pro = 1;
    rep1(i, n) {
        pro *= k + 1 - i;
        pro /= i;
        c[i] = pro;
    }
    uoo(n + 1);
    rep(i, n + 1) {
        cout << ans[i] << "\n";
    }
}
signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(10);
    //init_f();
    //init();
    //expr();
    //while(true)
    //int t; cin >> t; rep(i, t)
    solve();
    return 0;
}
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