結果

問題 No.444 旨味の相乗効果
コンテスト
ユーザー AngrySadEight
提出日時 2025-11-11 22:39:11
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 4 ms / 2,500 ms
コード長 6,267 bytes
コンパイル時間 4,255 ms
コンパイル使用メモリ 200,900 KB
実行使用メモリ 7,716 KB
最終ジャッジ日時 2025-11-11 22:39:17
合計ジャッジ時間 4,918 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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 * 5
other AC * 23
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 # 

#include <algorithm>
#include <atcoder/all>
#include <bitset>
#include <cassert>
#include <cmath>
#include <ctime>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using namespace atcoder;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--)
#define repk(i, k, n) for (int i = k; i < (int)(n); i++)
#define all(v) v.begin(), v.end()
#define mod1 1000000007
#define mod2 998244353
#define mod3 100000007
#define vi vector<int>
#define vs vector<string>
#define vc vector<char>
#define vl vector<ll>
#define vb vector<bool>
#define vvi vector<vector<int>>
#define vvc vector<vector<char>>
#define vvl vector<vector<ll>>
#define vvb vector<vector<bool>>
#define vvvi vector<vector<vector<int>>>
#define vvvl vector<vector<vector<ll>>>
#define pii pair<int, int>
#define pil pair<int, ll>
#define pli pair<ll, int>
#define pll pair<ll, ll>
#define vpii vector<pair<int, int>>
#define vpll vector<pair<ll, ll>>
#define vvpii vector<vector<pair<int, int>>>
#define vvpll vector<vector<pair<ll, ll>>>

template <typename T>
void debug(T e) {
    cerr << e << endl;
}

template <typename T>
void debug(vector<T> &v) {
    rep(i, v.size()) { cerr << v[i] << " "; }
    cerr << endl;
}

template <typename T>
void debug(vector<vector<T>> &v) {
    rep(i, v.size()) {
        rep(j, v[i].size()) { cerr << v[i][j] << " "; }
        cerr << endl;
    }
}

template <typename T>
void debug(vector<pair<T, T>> &v) {
    rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; }
}

template <typename T>
void debug(set<T> &st) {
    for (auto itr = st.begin(); itr != st.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}

template <typename T>
void debug(multiset<T> &ms) {
    for (auto itr = ms.begin(); itr != ms.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}

template <typename T>
void debug(map<T, T> &mp) {
    for (auto itr = mp.begin(); itr != mp.end(); itr++) {
        cerr << itr->first << " " << itr->second << endl;
    }
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << H << " ";
    debug_out(T...);
}

using mint = modint998244353;

void debug_mint1(vector<mint> &vec) {
    for (int i = 0; i < vec.size(); i++) {
        cerr << vec[i].val() << " ";
    }
    cerr << endl;
}

void debug_mint2(vector<vector<mint>> &vec) {
    for (int i = 0; i < vec.size(); i++) {
        for (int j = 0; j < vec[i].size(); j++) {
            cerr << vec[i][j].val() << " ";
        }
        cerr << endl;
    }
}


ll my_pow(ll x, ll n, ll mod) {
    // 　繰り返し二乗法．x^nをmodで割った余り．
    ll ret;
    if (n == 0) {
        ret = 1;
    } else if (n % 2 == 1) {
        ret = (x * my_pow((x * x) % mod, n / 2, mod)) % mod;
    } else {
        ret = my_pow((x * x) % mod, n / 2, mod);
    }
    return ret;
}

ll inv(ll x, ll mod) { return my_pow(x, mod - 2, mod); }

vector<ll> fps_inv(vector<ll> &f) {
    // f の mod 998244353 での fps_inv を返す
    ll n = f.size();
    ll new_n = 1;
    ll log = 0;
    while (new_n < n) {
        new_n *= 2;
        log++;
    }
    for (ll i = n; i < new_n; i++) {
        f.push_back(0);
    }
    // g[0] の項
    vector<ll> g = {inv(f[0], mod2)};
    ll now = 1;
    for (ll i = 0; i < log; i++) {
        now *= 2LL;
        vector<ll> fsub(now);
        for (ll j = 0; j < now; j++) {
            fsub[j] = f[j];
        }
        vector<ll> h1 = convolution(g, fsub);
        vector<ll> h2(now, 0);
        h2[0] = 2;
        for (ll j = 0; j < now; j++) {
            h2[j] = (h2[j] + mod2 - h1[j]) % mod2;
        }

        vector<ll> h3 = convolution(g, h2);
        for (ll j = 0; j < now / 2; j++) {
            g[j] = h3[j];
        }
        for (ll j = now / 2; j < now; j++) {
            g.push_back(h3[j]);
        }
    }
    vector<ll> new_g(0);
    for (ll i = 0; i < n; i++) {
        new_g.push_back(g[i]);
    }
    return new_g;
}

vector<ll> convolution_naive(vector<ll> &a, vector<ll> &b){
    ll len_a = a.size();
    ll len_b = b.size();
    vector<ll> c(len_a + len_b - 1);
    for (ll i = 0; i < len_a; i++){
        for (ll j = 0; j < len_b; j++){
            c[i + j] += a[i] * b[j];
            c[i + j] %= mod1;
        }
    }
    return c;
}

ll bostan_mori(vector<ll> &p, vector<ll> &q, ll n) {
    // bostan_mori 法を mod 998244353 で
    ll len_p = p.size();
    ll len_q = q.size();
    if (n == 0) {
        return (p[0] * inv(q[0], mod1)) % mod1;
    }
    vector<ll> q_minus(len_q);
    for (ll i = 0; i < len_q; i++) {
        if (i % 2 == 0) {
            q_minus[i] = q[i];
        } else {
            q_minus[i] = (mod1 - q[i]) % mod1;
        }
    }
    vector<ll> conv_p = convolution_naive(p, q_minus);
    vector<ll> conv_q = convolution_naive(q, q_minus);
    vector<ll> s(len_p);
    vector<ll> t(len_q);
    for (ll i = 0; i < len_q; i++) {
        t[i] = conv_q[i * 2];
    }
    if (n % 2 == 0) {
        for (ll i = 0; i < len_p; i++) {
            s[i] = conv_p[i * 2];
        }
    } else {
        for (ll i = 0; i < len_p; i++) {
            s[i] = conv_p[i * 2 + 1];
        }
    }
    return bostan_mori(s, t, n / 2);
}

int main() {
    ll n, c;
    cin >> n >> c;
    vector<ll> a(n);
    for (ll i = 0; i < n; i++){
        cin >> a[i];
    }
    queue<vector<ll>> que;
    for (ll i = 0; i < n; i++){
        que.push({1, (mod1 - a[i]) % mod1});
    }
    for (ll i = 0; i < n - 1; i++){
        vector<ll> v1 = que.front();
        que.pop();
        vector<ll> v2 = que.front();
        que.pop();
        vector<ll> v3 = convolution_naive(v1, v2);
        que.push(v3);
    }
    vector<ll> v = que.front();
    // debug(v);

    ll ans = 0;
    for (ll i = 0; i < n; i++){
        ans += (mod1 - my_pow(a[i], c, mod1));
        ans %= mod1;
    }
    vector<ll> v4(n, 0);
    v4[0] = 1;
    ans += bostan_mori(v4, v, c);
    ans %= mod1;
    cout << ans << endl;
}
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