結果

問題 No.1068 #いろいろな色 / Red and Blue and more various colors (Hard)
ユーザー yosupotyosupot
提出日時 2020-05-29 21:39:04
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 278 ms / 3,500 ms
コード長 22,290 bytes
コンパイル時間 1,954 ms
コンパイル使用メモリ 141,012 KB
実行使用メモリ 18,492 KB
最終ジャッジ日時 2024-11-06 02:55:25
合計ジャッジ時間 8,252 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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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
6,820 KB
testcase_01 AC 2 ms
6,820 KB
testcase_02 AC 2 ms
6,816 KB
testcase_03 AC 7 ms
6,816 KB
testcase_04 AC 4 ms
6,820 KB
testcase_05 AC 5 ms
6,816 KB
testcase_06 AC 4 ms
6,816 KB
testcase_07 AC 5 ms
6,816 KB
testcase_08 AC 5 ms
6,820 KB
testcase_09 AC 5 ms
6,816 KB
testcase_10 AC 3 ms
6,820 KB
testcase_11 AC 4 ms
6,816 KB
testcase_12 AC 3 ms
6,820 KB
testcase_13 AC 272 ms
18,364 KB
testcase_14 AC 276 ms
18,360 KB
testcase_15 AC 274 ms
18,364 KB
testcase_16 AC 269 ms
18,364 KB
testcase_17 AC 277 ms
18,492 KB
testcase_18 AC 273 ms
18,364 KB
testcase_19 AC 278 ms
18,364 KB
testcase_20 AC 275 ms
18,368 KB
testcase_21 AC 274 ms
18,364 KB
testcase_22 AC 274 ms
18,364 KB
testcase_23 AC 273 ms
18,492 KB
testcase_24 AC 274 ms
18,364 KB
testcase_25 AC 271 ms
18,368 KB
testcase_26 AC 273 ms
18,364 KB
testcase_27 AC 278 ms
18,364 KB
testcase_28 AC 223 ms
17,084 KB
testcase_29 AC 217 ms
17,080 KB
testcase_30 AC 216 ms
17,084 KB
testcase_31 AC 2 ms
6,820 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 # 

//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx")
//#undef LOCAL




#include <algorithm>

#include <array>

#include <bitset>

#include <cassert>

#include <complex>

#include <cstdio>

#include <cstring>

#include <iostream>

#include <map>

#include <numeric>

#include <queue>

#include <set>

#include <string>

#include <unordered_map>

#include <unordered_set>

#include <vector>

using namespace std;

using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;



#include <unistd.h>

struct Scanner {
    int fd = -1;
    char line[(1 << 15) + 1];
    size_t st = 0, ed = 0;
    void reread() {
        memmove(line, line + st, ed - st);
        ed -= st;
        st = 0;
        ed += ::read(fd, line + ed, (1 << 15) - ed);
        line[ed] = '\0';
    }
    bool succ() {
        while (true) {
            if (st == ed) {
                reread();
                if (st == ed) return false;
            }
            while (st != ed && isspace(line[st])) st++;
            if (st != ed) break;
        }
        if (ed - st <= 50) {
            bool sep = false;
            for (size_t i = st; i < ed; i++) {
                if (isspace(line[i])) {
                    sep = true;
                    break;
                }
            }
            if (!sep) reread();
        }
        return true;
    }
    template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
    bool read_single(T& ref) {
        if (!succ()) return false;
        while (true) {
            size_t sz = 0;
            while (st + sz < ed && !isspace(line[st + sz])) sz++;
            ref.append(line + st, sz);
            st += sz;
            if (!sz || st != ed) break;
            reread();
        }
        return true;
    }
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    bool read_single(T& ref) {
        if (!succ()) return false;
        bool neg = false;
        if (line[st] == '-') {
            neg = true;
            st++;
        }
        ref = T(0);
        while (isdigit(line[st])) {
            ref = 10 * ref + (line[st++] & 0xf);
        }
        if (neg) ref = -ref;
        return true;
    }
    template <class T> bool read_single(V<T>& ref) {
        for (auto& d : ref) {
            if (!read_single(d)) return false;
        }
        return true;
    }
    void read() {}
    template <class H, class... T> void read(H& h, T&... t) {
        bool f = read_single(h);
        assert(f);
        read(t...);
    }
    Scanner(FILE* fp) : fd(fileno(fp)) {}
};

struct Printer {
  public:
    template <bool F = false> void write() {}
    template <bool F = false, class H, class... T>
    void write(const H& h, const T&... t) {
        if (F) write_single(' ');
        write_single(h);
        write<true>(t...);
    }
    template <class... T> void writeln(const T&... t) {
        write(t...);
        write_single('\n');
    }

    Printer(FILE* _fp) : fp(_fp) {}
    ~Printer() { flush(); }

  private:
    static constexpr size_t SIZE = 1 << 15;
    FILE* fp;
    char line[SIZE], small[50];
    size_t pos = 0;
    void flush() {
        fwrite(line, 1, pos, fp);
        pos = 0;
    }
    void write_single(const char& val) {
        if (pos == SIZE) flush();
        line[pos++] = val;
    }
    template <class T, enable_if_t<is_integral<T>::value, int> = 0>
    void write_single(T val) {
        if (pos > (1 << 15) - 50) flush();
        if (val == 0) {
            write_single('0');
            return;
        }
        if (val < 0) {
            write_single('-');
            val = -val; // todo min
        }
        size_t len = 0;
        while (val) {
            small[len++] = char(0x30 | (val % 10));
            val /= 10;
        }
        for (size_t i = 0; i < len; i++) {
            line[pos + i] = small[len - 1 - i];
        }
        pos += len;
    }
    void write_single(const string& s) {
        for (char c : s) write_single(c);
    }
    void write_single(const char* s) {
        size_t len = strlen(s);
        for (size_t i = 0; i < len; i++) write_single(s[i]);
    }
    template <class T> void write_single(const V<T>& val) {
        auto n = val.size();
        for (size_t i = 0; i < n; i++) {
            if (i) write_single(' ');
            write_single(val[i]);
        }
    }
};



template <uint MD> struct ModInt {
    using M = ModInt;
    static constexpr uint get_mod() { return MD; }
    const static M G;
    uint v;
    ModInt(ll _v = 0) { set_v(uint(_v % MD + MD)); }
    M& set_v(uint _v) {
        v = (_v < MD) ? _v : _v - MD;
        return *this;
    }
    explicit operator bool() const { return v != 0; }
    M operator-() const { return M() - *this; }
    M operator+(const M& r) const { return M().set_v(v + r.v); }
    M operator-(const M& r) const { return M().set_v(v + MD - r.v); }
    M operator*(const M& r) const { return M().set_v(uint(ull(v) * r.v % MD)); }
    M operator/(const M& r) const { return *this * r.inv(); }
    M& operator+=(const M& r) { return *this = *this + r; }
    M& operator-=(const M& r) { return *this = *this - r; }
    M& operator*=(const M& r) { return *this = *this * r; }
    M& operator/=(const M& r) { return *this = *this / r; }
    bool operator==(const M& r) const { return v == r.v; }
    M pow(ll n) const {
        M x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    M inv() const { return pow(MD - 2); }
    friend ostream& operator<<(ostream& os, const M& r) { return os << r.v; }
};
// using Mint = ModInt<998244353>;
// template<> const Mint Mint::G = Mint(3);
using Mint = ModInt<998244353>;
template<> const Mint Mint::G = Mint(3);





// bit op
int popcnt(uint x) { return __builtin_popcount(x); }
int popcnt(ull x) { return __builtin_popcountll(x); }
int bsr(uint x) { return 31 - __builtin_clz(x); }
int bsr(ull x) { return 63 - __builtin_clzll(x); }
int bsf(uint x) { return __builtin_ctz(x); }
int bsf(ull x) { return __builtin_ctzll(x); }

template <class Mint> void nft(bool type, V<Mint>& a) {
    int n = int(a.size()), s = 0;
    while ((1 << s) < n) s++;
    assert(1 << s == n);

    static V<Mint> ep, iep;
    while (int(ep.size()) <= s) {
        ep.push_back(Mint::G.pow(Mint(-1).v / (1 << ep.size())));
        iep.push_back(ep.back().inv());
    }
    V<Mint> b(n);
    for (int i = 1; i <= s; i++) {
        int w = 1 << (s - i);
        Mint base = type ? iep[i] : ep[i], now = 1;
        for (int y = 0; y < n / 2; y += w) {
            for (int x = 0; x < w; x++) {
                auto l = a[y << 1 | x];
                auto r = now * a[y << 1 | x | w];
                b[y | x] = l + r;
                b[y | x | n >> 1] = l - r;
            }
            now *= base;
        }
        swap(a, b);
    }
}

template <class Mint> V<Mint> multiply_nft(const V<Mint>& a, const V<Mint>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (min(n, m) <= 8) {
        V<Mint> ans(n + m - 1);
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++) ans[i + j] += a[i] * b[j];
        return ans;
    }
    int lg = 0;
    while ((1 << lg) < n + m - 1) lg++;
    int z = 1 << lg;
    auto a2 = a, b2 = b;
    a2.resize(z);
    b2.resize(z);
    nft(false, a2);
    nft(false, b2);
    for (int i = 0; i < z; i++) a2[i] *= b2[i];
    nft(true, a2);
    a2.resize(n + m - 1);
    Mint iz = Mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a2[i] *= iz;
    return a2;
}

// Cooley-Tukey: input -> butterfly -> bit reversing -> output から
// bit reversingを抜いたもの 直接使うな
template <class Mint> void butterfly(bool type, V<Mint>& a) {
    int n = int(a.size()), h = 0;
    while ((1 << h) < n) h++;
    assert(1 << h == n);
    if (n == 1) return;

    static V<Mint> snow, sinow;
    if (snow.empty()) {
        Mint sep = Mint(1), siep = Mint(1);
        uint mod = Mint(-1).v;
        uint di = 4;
        while (mod % di == 0) {
            Mint ep = Mint::G.pow(mod / di);
            Mint iep = ep.inv();
            snow.push_back(siep * ep);
            sinow.push_back(sep * iep);
            sep *= ep;
            siep *= iep;
            di *= 2;
        }
    }

    if (!type) {
        // fft
        for (int ph = 1; ph <= h; ph++) {
            // phase ph: size w -> 2w の FFT, p 並列
            int w = 1 << (ph - 1), p = 1 << (h - ph);
            Mint now = Mint(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;
                }
                int u = bsf(~uint(s));
                now *= snow[u];
            }
        }
    } else {
        // ifft
        for (int ph = h; ph >= 1; ph--) {
            int w = 1 << (ph - 1), p = 1 << (h - ph);
            Mint inow = Mint(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] = (l - r) * inow;
                }
                int u = bsf(~uint(s));
                inow *= sinow[u];
            }
        }
    }
}

template <class Mint> V<Mint> multiply(const V<Mint>& a, const V<Mint>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (min(n, m) < 8) {
        V<Mint> ans(n + m - 1);
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++) ans[i + j] += a[i] * b[j];
        return ans;
    }
    int lg = 0;
    while ((1 << lg) < n + m - 1) lg++;
    int z = 1 << lg;
    auto a2 = a;
    a2.resize(z);
    butterfly(false, a2);
    if (a == b) {
        for (int i = 0; i < z; i++) a2[i] *= a2[i];
    } else {
        auto b2 = b;
        b2.resize(z);
        butterfly(false, b2);
        for (int i = 0; i < z; i++) a2[i] *= b2[i];
    }
    butterfly(true, a2);
    a2.resize(n + m - 1);
    Mint iz = Mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a2[i] *= iz;
    return a2;
}








#include <chrono>

#include <cstdint>


#include <random>



struct Random {
  private:
    // Use xoshiro256**
    // Refereces: http://xoshiro.di.unimi.it/xoshiro256starstar.c
    static uint64_t rotl(const uint64_t x, int k) {
        return (x << k) | (x >> (64 - k));
    }

    std::array<uint64_t, 4> s;

    uint64_t next() {
        const uint64_t result_starstar = rotl(s[1] * 5, 7) * 9;

        const uint64_t t = s[1] << 17;

        s[2] ^= s[0];
        s[3] ^= s[1];
        s[1] ^= s[2];
        s[0] ^= s[3];

        s[2] ^= t;

        s[3] = rotl(s[3], 45);

        return result_starstar;
    }

    // random choice from [0, upper]
    uint64_t next(uint64_t upper) {
        if (!(upper & (upper + 1))) {
            // b = 00..0011..11
            return next() & upper;
        }
        int lg = 63 - __builtin_clzll(upper);
        uint64_t mask = (lg == 63) ? ~0ULL : (1ULL << (lg + 1)) - 1;
        while (true) {
            uint64_t r = next() & mask;
            if (r <= upper) return r;
        }
    }

  public:
    Random(uint64_t seed = 0) {
        // Use splitmix64
        // Reference: http://xoshiro.di.unimi.it/splitmix64.c
        for (int i = 0; i < 4; i++) {
            uint64_t z = (seed += 0x9e3779b97f4a7c15);
            z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
            z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
            s[i] = z ^ (z >> 31);
        }
    }

    // random choice from [lower, upper]
    template <class T> T uniform(T lower, T upper) {
        assert(lower <= upper);
        return T(lower + next(uint64_t(upper - lower)));
    }

    bool uniform_bool() { return uniform(0, 1) == 1; }

    double uniform01() {
        uint64_t v = next(1ULL << 63);
        return double(v) / (1ULL << 63);
    }

    template <class T> std::pair<T, T> uniform_pair(T lower, T upper) {
        assert(upper - lower >= 1);
        T a, b;
        do {
            a = uniform(lower, upper);
            b = uniform(lower, upper);
        } while (a == b);
        if (a > b) std::swap(a, b);
        return {a, b};
    }

    // generate random lower string that length = n
    std::string lower_string(size_t n) {
        std::string res = "";
        for (size_t i = 0; i < n; i++) {
            res += uniform('a', 'z');
        }
        return res;
    }

    // random shuffle
    template <class Iter> void shuffle(Iter first, Iter last) {
        if (first == last) return;
        // Reference and edit:
        // cpprefjp - C++日本語リファレンス
        // (https://cpprefjp.github.io/reference/algorithm/shuffle.html)
        int len = 1;
        for (auto it = first + 1; it != last; it++) {
            len++;
            int j = uniform(0, len - 1);
            if (j != len - 1) iter_swap(it, first + j);
        }
    }

    // generate random permutation that length = n
    template <class T> std::vector<T> perm(size_t n) {
        std::vector<T> idx(n);
        std::iota(idx.begin(), idx.end(), T(0));
        shuffle(idx.begin(), idx.end());
        return idx;
    }

    template <class T> std::vector<T> choice(size_t n, T lower, T upper) {
        assert(n <= upper - lower + 1);
        std::set<T> res;
        while (res.size() < n) res.insert(uniform(lower, upper));
        return {res.begin(), res.end()};
    }
};
Random& global_gen() {
    static Random gen;
    return gen;
}
Random get_random_gen() {
    return Random(chrono::steady_clock::now().time_since_epoch().count());
}
Random& global_runtime_gen() {
    static Random gen = get_random_gen();
    return gen;
}
template <class D> struct Poly {
    V<D> v;
    Poly(const V<D>& _v = {}) : v(_v) { shrink(); }
    void shrink() {
        while (v.size() && !v.back()) v.pop_back();
    }

    int size() const { return int(v.size()); }
    D freq(int p) const { return (p < size()) ? v[p] : D(0); }

    Poly operator+(const Poly& r) const {
        auto n = max(size(), r.size());
        V<D> res(n);
        for (int i = 0; i < n; i++) res[i] = freq(i) + r.freq(i);
        return res;
    }
    Poly operator-(const Poly& r) const {
        int n = max(size(), r.size());
        V<D> res(n);
        for (int i = 0; i < n; i++) res[i] = freq(i) - r.freq(i);
        return res;
    }
    Poly operator*(const Poly& r) const { return {multiply(v, r.v)}; }
    Poly operator*(const D& r) const {
        int n = size();
        V<D> res(n);
        for (int i = 0; i < n; i++) res[i] = v[i] * r;
        return res;
    }
    Poly operator/(const D &r) const{
        return *this * r.inv();
    }
    Poly operator/(const Poly& r) const {
        if (size() < r.size()) return {{}};
        int n = size() - r.size() + 1;
        return (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
    }
    Poly operator%(const Poly& r) const { return *this - *this / r * r; }
    Poly operator<<(int s) const {
        V<D> res(size() + s);
        for (int i = 0; i < size(); i++) res[i + s] = v[i];
        return res;
    }
    Poly operator>>(int s) const {
        if (size() <= s) return Poly();
        V<D> res(size() - s);
        for (int i = 0; i < size() - s; i++) res[i] = v[i + s];
        return res;
    }
    Poly& operator+=(const Poly& r) { return *this = *this + r; }
    Poly& operator-=(const Poly& r) { return *this = *this - r; }
    Poly& operator*=(const Poly& r) { return *this = *this * r; }
    Poly& operator*=(const D& r) { return *this = *this * r; }
    Poly& operator/=(const Poly& r) { return *this = *this / r; }
    Poly& operator/=(const D &r) {return *this = *this/r;}
    Poly& operator%=(const Poly& r) { return *this = *this % r; }
    Poly& operator<<=(const size_t& n) { return *this = *this << n; }
    Poly& operator>>=(const size_t& n) { return *this = *this >> n; }

    Poly pre(int le) const {
        return {{v.begin(), v.begin() + min(size(), le)}};
    }
    Poly rev(int n = -1) const {
        V<D> res = v;
        if (n != -1) res.resize(n);
        reverse(res.begin(), res.end());
        return res;
    }
    Poly diff() const {
        V<D> res(max(0, size() - 1));
        for (int i = 1; i < size(); i++) res[i - 1] = freq(i) * i;
        return res;
    }
    Poly inte() const {
        V<D> res(size() + 1);
        for (int i = 0; i < size(); i++) res[i + 1] = freq(i) / (i + 1);
        return res;
    }

    // f * f.inv() = 1 + g(x)x^m
    Poly inv(int m) const {
        Poly res = Poly({D(1) / freq(0)});
        for (int i = 1; i < m; i *= 2) {
            res = (res * D(2) - res * res * pre(2 * i)).pre(2 * i);
        }
        return res.pre(m);
    }
    Poly exp(int n) const {
        assert(freq(0) == 0);
        Poly f({1}), g({1});
        for (int i = 1; i < n; i *= 2) {
            g = (g * 2 - f * g * g).pre(i);
            Poly q = diff().pre(i - 1);
            Poly w = (q + g * (f.diff() - f * q)).pre(2 * i - 1);
            f = (f + f * (*this - w.inte()).pre(2 * i)).pre(2 * i);
        }
        return f.pre(n);
    }
    Poly log(int n) const {
        assert(freq(0) == 1);
        auto f = pre(n);
        return (f.diff() * f.inv(n - 1)).pre(n - 1).inte();
    }
    Poly sqrt(int n) const {
        assert(freq(0) == 1);
        Poly f = pre(n + 1);
        Poly g({1});
        for (int i = 1; i < n; i *= 2) {
            g = (g + f.pre(2 * i) * g.inv(2 * i)) / 2;
        }
        return g.pre(n + 1);
    }

    Poly pow_mod(ll n, const Poly& mod) {
        Poly x = *this, r = {{1}};
        while (n) {
            if (n & 1) r = r * x % mod;
            x = x * x % mod;
            n >>= 1;
        }
        return r;
    }

    friend ostream& operator<<(ostream& os, const Poly& p) {
        if (p.size() == 0) return os << "0";
        for (auto i = 0; i < p.size(); i++) {
            if (p.v[i]) {
                os << p.v[i] << "x^" << i;
                if (i != p.size() - 1) os << "+";
            }
        }
        return os;
    }
};

template <class Mint> struct MultiEval {
    using NP = MultiEval*;
    NP l, r;
    V<Mint> que;
    int sz;
    Poly<Mint> mul;
    MultiEval(const V<Mint>& _que, int off, int _sz) : sz(_sz) {
        if (sz <= 100) {
            que = {_que.begin() + off, _que.begin() + off + sz};
            mul = {{1}};
            for (auto x : que) mul *= {{-x, 1}};
            return;
        }
        l = new MultiEval(_que, off, sz / 2);
        r = new MultiEval(_que, off + sz / 2, sz - sz / 2);
        mul = l->mul * r->mul;
    }
    MultiEval(const V<Mint>& _que) : MultiEval(_que, 0, int(_que.size())) {}
    void query(const Poly<Mint>& _pol, V<Mint>& res) const {
        if (sz <= 100) {
            for (auto x : que) {
                Mint sm = 0, base = 1;
                for (int i = 0; i < _pol.size(); i++) {
                    sm += base * _pol.freq(i);
                    base *= x;
                }
                res.push_back(sm);
            }
            return;
        }
        auto pol = _pol % mul;
        l->query(pol, res);
        r->query(pol, res);
    }
    V<Mint> query(const Poly<Mint>& pol) const {
        V<Mint> res;
        query(pol, res);
        return res;
    }
};

template <class Mint> Poly<Mint> berlekamp_massey(const V<Mint>& s) {
    int n = int(s.size());
    V<Mint> b = {Mint(-1)}, c = {Mint(-1)};
    Mint y = Mint(1);
    for (int ed = 1; ed <= n; ed++) {
        int l = int(c.size()), m = int(b.size());
        Mint x = 0;
        for (int i = 0; i < l; i++) {
            x += c[i] * s[ed - l + i];
        }
        b.push_back(0);
        m++;
        if (!x) continue;
        Mint freq = x / y;
        if (l < m) {
            // use b
            auto tmp = c;
            c.insert(begin(c), m - l, Mint(0));
            for (int i = 0; i < m; i++) {
                c[m - 1 - i] -= freq * b[m - 1 - i];
            }
            b = tmp;
            y = x;
        } else {
            // use c
            for (int i = 0; i < m; i++) {
                c[l - 1 - i] -= freq * b[m - 1 - i];
            }
        }
    }
    return c;
}

template <class E, class Mint = decltype(E().f)>
Mint sparse_det(const VV<E>& g) {
    int n = int(g.size());
    if (n == 0) return 1;
    auto rand_v = [&]() {
        V<Mint> res(n);
        for (int i = 0; i < n; i++) {
            res[i] = Mint(global_gen().uniform<int>(1, Mint::get_mod() - 1));
        }
        return res;
    };
    V<Mint> c = rand_v(), l = rand_v(), r = rand_v();
    // l * mat * r
    V<Mint> buf(2 * n);
    for (int fe = 0; fe < 2 * n; fe++) {
        for (int i = 0; i < n; i++) {
            buf[fe] += l[i] * r[i];
        }
        for (int i = 0; i < n; i++) {
            r[i] *= c[i];
        }
        V<Mint> tmp(n);
        for (int i = 0; i < n; i++) {
            for (auto e : g[i]) {
                tmp[i] += r[e.to] * e.f;
            }
        }
        r = tmp;
    }
    auto u = berlekamp_massey(buf);
    if (u.size() != n + 1) return sparse_det(g);
    auto acdet = u.freq(0) * Mint(-1);
    if (n % 2) acdet *= Mint(-1);
    if (!acdet) return 0;
    Mint cdet = 1;
    for (int i = 0; i < n; i++) cdet *= c[i];
    return acdet / cdet;
}
using MPol = Poly<Mint>;

Scanner sc = Scanner(stdin);
Printer pr = Printer(stdout);

int main() {
    int n, q;
    sc.read(n, q);

    V<MPol> pols(n);
    for (int i = 0; i < n; i++) {
        ll a;
        sc.read(a);
        pols[i] = {{Mint(a - 1), Mint(1)}};
    }

    auto mul = [&](auto self, int l, int r) -> MPol {
        if (l + 1 == r) return pols[l];
        int md = (l + r) / 2;
        return self(self, l, md) * self(self, md, r);
    };

    auto ans = mul(mul, 0, n);
    for (int i = 0; i < q; i++) {
        int b;
        sc.read(b);
        pr.writeln(ans.freq(b).v);
    }
    return 0;
}
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