結果

問題 No.2025 Select $k$-th Submultiset
ユーザー tokusakuraitokusakurai
提出日時 2022-07-29 22:52:23
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 461 ms / 2,000 ms
コード長 9,884 bytes
コンパイル時間 3,063 ms
コンパイル使用メモリ 235,308 KB
実行使用メモリ 18,268 KB
最終ジャッジ日時 2024-07-19 16:07:31
合計ジャッジ時間 14,739 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,816 KB
testcase_01 AC 2 ms
6,944 KB
testcase_02 AC 20 ms
6,940 KB
testcase_03 AC 461 ms
18,268 KB
testcase_04 AC 420 ms
18,268 KB
testcase_05 AC 408 ms
13,976 KB
testcase_06 AC 334 ms
13,440 KB
testcase_07 AC 349 ms
15,608 KB
testcase_08 AC 306 ms
14,072 KB
testcase_09 AC 409 ms
16,820 KB
testcase_10 AC 447 ms
15,516 KB
testcase_11 AC 357 ms
11,980 KB
testcase_12 AC 448 ms
15,952 KB
testcase_13 AC 328 ms
14,844 KB
testcase_14 AC 340 ms
13,952 KB
testcase_15 AC 405 ms
15,524 KB
testcase_16 AC 353 ms
13,496 KB
testcase_17 AC 353 ms
15,864 KB
testcase_18 AC 355 ms
13,552 KB
testcase_19 AC 390 ms
12,964 KB
testcase_20 AC 355 ms
13,280 KB
testcase_21 AC 301 ms
14,804 KB
testcase_22 AC 312 ms
12,360 KB
testcase_23 AC 401 ms
14,220 KB
testcase_24 AC 341 ms
13,832 KB
testcase_25 AC 2 ms
6,940 KB
testcase_26 AC 2 ms
6,940 KB
testcase_27 AC 2 ms
6,940 KB
testcase_28 AC 2 ms
6,940 KB
testcase_29 AC 2 ms
6,940 KB
testcase_30 AC 2 ms
6,944 KB
testcase_31 AC 2 ms
6,944 KB
testcase_32 AC 2 ms
6,940 KB
testcase_33 AC 2 ms
6,944 KB
testcase_34 AC 2 ms
6,940 KB
testcase_35 AC 2 ms
6,944 KB
testcase_36 AC 2 ms
6,944 KB
testcase_37 AC 2 ms
6,940 KB
testcase_38 AC 2 ms
6,944 KB
testcase_39 AC 2 ms
6,944 KB
testcase_40 AC 2 ms
6,944 KB
testcase_41 AC 2 ms
6,940 KB
testcase_42 AC 2 ms
6,944 KB
testcase_43 AC 2 ms
6,940 KB
testcase_44 AC 2 ms
6,940 KB
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 <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)
#define rep2(i, x, n) for (int i = x; i <= n; i++)
#define rep3(i, x, n) for (int i = x; i >= n; i--)
#define each(e, v) for (auto &e : v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
const int MOD = 1000000007;
// const int MOD = 998244353;

template <int mod>
struct Mod_Int {
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    static int get_mod() { return mod; }

    Mod_Int &operator+=(const Mod_Int &p) {
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator-=(const Mod_Int &p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator*=(const Mod_Int &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    Mod_Int &operator/=(const Mod_Int &p) {
        *this *= p.inverse();
        return *this;
    }

    Mod_Int &operator++() { return *this += Mod_Int(1); }

    Mod_Int operator++(int) {
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int &operator--() { return *this -= Mod_Int(1); }

    Mod_Int operator--(int) {
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Mod_Int operator-() const { return Mod_Int(-x); }

    Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }

    Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }

    Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }

    Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }

    bool operator==(const Mod_Int &p) const { return x == p.x; }

    bool operator!=(const Mod_Int &p) const { return x != p.x; }

    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod - 2);
    }

    Mod_Int pow(long long k) const {
        Mod_Int now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }

    friend istream &operator>>(istream &is, Mod_Int &p) {
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};

using mint = Mod_Int<MOD>;

template <typename T>
struct Number_Theoretic_Transform {
    static int max_base;
    static T root;
    static vector<T> r, ir;

    Number_Theoretic_Transform() {}

    static void init() {
        if (!r.empty()) return;
        int mod = T::get_mod();
        int tmp = mod - 1;
        root = 2;
        while (root.pow(tmp >> 1) == 1) root++;
        max_base = 0;
        while (tmp % 2 == 0) tmp >>= 1, max_base++;
        r.resize(max_base), ir.resize(max_base);
        for (int i = 0; i < max_base; i++) {
            r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i]  := 1 の 2^(i+2) 乗根
            ir[i] = r[i].inverse();                 // ir[i] := 1/r[i]
        }
    }

    static void ntt(vector<T> &a) {
        init();
        int n = a.size();
        assert((n & (n - 1)) == 0);
        assert(n <= (1 << max_base));
        for (int k = n; k >>= 1;) {
            T w = 1;
            for (int s = 0, t = 0; s < n; s += 2 * k) {
                for (int i = s, j = s + k; i < s + k; i++, j++) {
                    T x = a[i], y = w * a[j];
                    a[i] = x + y, a[j] = x - y;
                }
                w *= r[__builtin_ctz(++t)];
            }
        }
    }

    static void intt(vector<T> &a) {
        init();
        int n = a.size();
        assert((n & (n - 1)) == 0);
        assert(n <= (1 << max_base));
        for (int k = 1; k < n; k <<= 1) {
            T w = 1;
            for (int s = 0, t = 0; s < n; s += 2 * k) {
                for (int i = s, j = s + k; i < s + k; i++, j++) {
                    T x = a[i], y = a[j];
                    a[i] = x + y, a[j] = w * (x - y);
                }
                w *= ir[__builtin_ctz(++t)];
            }
        }
        T inv = T(n).inverse();
        for (auto &e : a) e *= inv;
    }

    static vector<T> convolve(vector<T> a, vector<T> b) {
        if (a.empty() || b.empty()) return {};
        int k = (int)a.size() + (int)b.size() - 1, n = 1;
        while (n < k) n <<= 1;
        a.resize(n), b.resize(n);
        ntt(a), ntt(b);
        for (int i = 0; i < n; i++) a[i] *= b[i];
        intt(a), a.resize(k);
        return a;
    }
};

template <typename T>
int Number_Theoretic_Transform<T>::max_base = 0;

template <typename T>
T Number_Theoretic_Transform<T>::root = T();

template <typename T>
vector<T> Number_Theoretic_Transform<T>::r = vector<T>();

template <typename T>
vector<T> Number_Theoretic_Transform<T>::ir = vector<T>();

using NTT = Number_Theoretic_Transform<mint>;

const int m1 = 880803841; // 105*2^23 + 1
const int m2 = 897581057; // 107*2^23 + 1
const int m3 = 998244353; // 119*2^23 + 1

struct Fast_Fourier_Transform_Integer {
    using mint_1 = Mod_Int<m1>;
    using mint_2 = Mod_Int<m2>;
    using mint_3 = Mod_Int<m3>;
    using NTT_1 = Number_Theoretic_Transform<mint_1>;
    using NTT_2 = Number_Theoretic_Transform<mint_2>;
    using NTT_3 = Number_Theoretic_Transform<mint_3>;

    Fast_Fourier_Transform_Integer() {}

    static vector<long long> convolve(const vector<long long> &a, const vector<long long> &b) {
        if (a.empty() || b.empty()) return {};
        int n = a.size(), m = b.size();
        vector<mint_1> a1(n), b1(m);
        vector<mint_2> a2(n), b2(m);
        vector<mint_3> a3(n), b3(m);
        for (int i = 0; i < n; i++) a1[i] = a[i], a2[i] = a[i], a3[i] = a[i];
        for (int i = 0; i < m; i++) b1[i] = b[i], b2[i] = b[i], b3[i] = b[i];
        vector<mint_1> c1 = NTT_1::convolve(a1, b1);
        vector<mint_2> c2 = NTT_2::convolve(a2, b2);
        vector<mint_3> c3 = NTT_3::convolve(a3, b3);
        mint_2 m1_inv_m2 = mint_2(m1).inverse();
        mint_3 m1m2_inv_m3 = (mint_3(m1) * m2).inverse();
        vector<long long> c(n + m - 1);
        for (int i = 0; i < n + m - 1; i++) {
            long long t1 = (m1_inv_m2 * (c2[i].x - c1[i].x)).x;
            long long t = (m1m2_inv_m3 * (c3[i].x - t1 * m1 - c1[i].x)).x;
            if (t > m3 - t) t -= m3;
            c[i] = t * m1 * m2 + t1 * m1 + c1[i].x;
        }
        return c;
    }
};

Fast_Fourier_Transform_Integer FFT;

int main() {
    int N, L;
    cin >> N >> L;

    vector<int> c(N);
    rep(i, N) cin >> c[i];

    vector<vector<ll>> dp(N + 1);
    dp[N].assign(L + 1, 0);
    dp[N][0] = 1;
    rep3(i, N - 1, 0) {
        dp[i].assign(c[i] + 1, 1);
        dp[i] = FFT.convolve(dp[i], dp[i + 1]);
        dp[i].resize(L + 1);
    }

    rep(i, N + 1) {
        rep3(j, L - 1, 0) dp[i][j] += dp[i][j + 1]; //
    }

    int Q;
    cin >> Q;

    while (Q--) {
        ll X;
        cin >> X;

        if (X > dp[0][L]) {
            cout << "-1\n";
            continue;
        }

        vector<ll> ans(N);
        int R = L;

        rep(i, N) {
            int l = -1, r = min(R, c[i]);
            int T = r;
            while (r - l > 1) {
                int m = (l + r) / 2;
                if (dp[i + 1][R - T] - dp[i + 1][R - m] < X) {
                    r = m;
                } else {
                    l = m;
                }
            }
            ans[i] = r;
            X -= dp[i + 1][R - T] - dp[i + 1][R - r];
            R -= r;
        }

        print(ans);
    }
}
0