#1148517 (C++17) No.8046 yukicoderの過去問

• 問題: No.8046 yukicoderの過去問
• ユーザー: AngrySadEight
• 提出日時: 2026-02-19 00:30:55
• 言語: C++17 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 531 ms / 2,000 ms
• コード長: 6,227 bytes
• コンパイル時間: 4,615 ms
• コンパイル使用メモリ: 233,168 KB
• 実行使用メモリ: 16,004 KB
• 最終ジャッジ日時: 2026-02-19 00:31:04
• 合計ジャッジ時間: 8,229 ms
• ジャッジサーバーID （参考情報）: judge5 / judge4

ファイルパターン	結果
other	AC * 9

ソースコード

#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); }

ll garner(vector<pll> &mr, ll mod, vector<ll> &coff_inv){
    mr.push_back(make_pair(mod, 0));

    vector<ll> coffs(mr.size(), 1);
    vector<ll> constants(mr.size(), 0);
    for (ll i = 0; i < mr.size() - 1; i++){
        ll v = (mr[i].second + mr[i].first - constants[i]) * coff_inv[i];
        v %= mr[i].first;
        if (v < 0){
            v += mr[i].first;
        }
        for (ll j = i + 1; j < mr.size(); j++){
            constants[j] += coffs[j] * v;
            constants[j] %= mr[j].first;
            coffs[j] *= mr[i].first;
            coffs[j] %= mr[j].first;
        }
    }
    return constants[mr.size() - 1];
}

vector<ll> conv_freemod(vector<ll> &a, vector<ll> &b, ll mod){
    ll m1 = 998244353;
    ll m2 = 167772161;
    ll m3 = 469762049;

    vector<ll> c1 = convolution<998244353>(a, b);
    vector<ll> c2 = convolution<167772161>(a, b);
    vector<ll> c3 = convolution<469762049>(a, b);

    vector<ll> mods = {m1, m2, m3};

    vector<ll> coffs(3, 1);
    for (ll i = 0; i < 2; i++){
        for (ll j = i + 1; j < 3; j++){
            coffs[j] *= mods[i];
            coffs[j] %= mods[j];
        }
    }
    vector<ll> coff_inv(3);
    for (ll i = 0; i < 3; i++){
        coff_inv[i] = inv(coffs[i], mods[i]);
    }

    vector<ll> c(c1.size());
    for (ll i = 0; i < c1.size(); i++){
        vector<pll> p;
        p.push_back(make_pair(m1, c1[i]));
        p.push_back(make_pair(m2, c2[i]));
        p.push_back(make_pair(m3, c3[i]));

        ll g = garner(p, mod, coff_inv);
        
        c[i] = g;
    }
    return c;
}

vector<ll> fps_inv(vector<ll> &f, ll mod) {
    // 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], mod)};
    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 = conv_freemod(g, fsub, mod);
        vector<ll> h2(now, 0);
        h2[0] = 2;
        for (ll j = 0; j < now; j++) {
            h2[j] = (h2[j] + mod - h1[j]) % mod;
        }

        vector<ll> h3 = conv_freemod(g, h2, mod);
        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;
}


int main() {
    ll N;
    cin >> N;
    ll K;
    cin >> K;
    vector<ll> x(K);
    rep(i, K){
        cin >> x[i];
    }
    vector<ll> bumbo(N + 2);
    bumbo[0] = 1;
    for (ll i = 0; i < K; i++){
        if (x[i] <= N + 1){
            bumbo[x[i]] = mod1 - 1;
        }
    }
    vector<ll> inv_vec = fps_inv(bumbo, mod1);
    cout << inv_vec[N] << endl;
}