結果

問題 No.8120 Aoki's Present for Takahashi
ユーザー 👑 Nachia
提出日時 2025-04-01 22:34:27
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 173 ms / 2,000 ms
コード長 6,691 bytes
コンパイル時間 1,346 ms
コンパイル使用メモリ 94,100 KB
実行使用メモリ 12,164 KB
最終ジャッジ日時 2025-04-01 23:16:09
合計ジャッジ時間 5,457 ms
ジャッジサーバーID
(参考情報)
judge2 / judge6
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 1
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 #

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(i64 i=0; i<i64(n); i++)
const i64 INF = 1001001001001001001;
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;

#include <atcoder/modint>
#include <cassert>

#include <utility>
namespace nachia{

// ax + by = gcd(a,b)
// return ( x, - )
std::pair<long long, long long> ExtGcd(long long a, long long b){
    long long x = 1, y = 0;
    while(b){
        long long u = a / b;
        std::swap(a-=b*u, b);
        std::swap(x-=y*u, y);
    }
    return std::make_pair(x, a);
}

} // namespace nachia

namespace nachia{

class DynamicModSupplier{
    using u64 = unsigned long long;
    using Int = unsigned int;
private:
    u64 imod;
    Int mod;
    // atcoder library
    u64 reduce2(u64 z) const noexcept {
        // atcoder library
#ifdef _MSC_VER
        u64 x; _umul128(z, im, &x);
#else
        using u128 = unsigned __int128;
        u64 x = (u64)(((u128)(z)*imod) >> 64);
#endif
        return z - x * mod;
    }
public:
    DynamicModSupplier(unsigned int MOD = 998244353) : mod(MOD) {
        assert(2 <= MOD);
        assert(MOD < (1u << 31));
        imod = (u64)(-1) / mod + 1;
    }
    Int reduce(u64 z) const noexcept {
        Int v = reduce2(z);
        if(mod <= v) v += mod;
        return v;
    }
    Int add(Int a, Int b) const { a += b; if(a >= mod){ a -= mod; } return a; }
    Int sub(Int a, Int b) const { a -= b; if(a >= mod){ a += mod; } return a; }
    Int mul(Int a, Int b) const { return reduce((u64)a * b); }
    Int muladd(Int a, Int b, Int c) const { return reduce((u64)a * b + c); }
    Int inv(Int a) const {
        Int v = ExtGcd(a, mod).first;
        return (v < mod) ? v : (v + mod);
    }
    Int pow(Int a, u64 i) const {
        Int r = a, ans = 1;
        while(i){
            if(i & 1) ans = mul(ans, r);
            i /= 2;
            r = mul(r, r);
        }
        return ans;
    }
    Int getMod() const { return mod; }
};

} // namespace nachia

namespace nachia{

template<class FinishType>
struct GarnerMod{
    using Int = unsigned int;
    using IntLong = unsigned long long;
    std::vector<Int> mods;
    std::vector<DynamicModSupplier> dynmods;
    std::vector<std::vector<Int>> table_coeff;
    std::vector<Int> table_coeffinv;

    void precalc(std::vector<Int> new_mods){
        mods = std::move(new_mods);
        dynmods.resize(mods.size());
        for(size_t i=0; i<mods.size(); i++) dynmods[i] = DynamicModSupplier(mods[i]);
        int nmods = mods.size();
        table_coeff.assign(nmods+1, std::vector<Int>(nmods, 1));
        for(int j=0; j<nmods; j++){
            for(int k=0; k<nmods; k++) table_coeff[j+1][k] = table_coeff[j][k];
            for(int k=j+1; k<nmods; k++) table_coeff[j+1][k] = dynmods[k].mul(table_coeff[j+1][k], mods[j] % mods[k]);
        }
        table_coeffinv.resize(nmods);
        for(int i=0; i<nmods; i++) table_coeffinv[i] = dynmods[i].inv(table_coeff[i][i]);
    }

    FinishType calc(const std::vector<Int>& x) const {
        int nmods = mods.size();
        std::vector<Int> table_const(nmods);
        FinishType res = 0;
        FinishType res_coeff = 1;
        for(int j=0; j<nmods; j++){
            Int t = dynmods[j].mul(dynmods[j].sub(x[j], table_const[j]), table_coeffinv[j]);
            for(int k=j+1; k<nmods; k++){
                table_const[k] = dynmods[k].muladd(t, table_coeff[j][k], table_const[k]);
            }
            res += res_coeff * FinishType(t);
            res_coeff *= mods[j];
        }
        return res;
    }

    std::vector<FinishType> calc(std::vector<std::vector<Int>> x) const {
        int n = x[0].size(), m = x.size();
        std::vector<FinishType> res(n);
        std::vector<Int> buf(m);
        for(int i=0; i<n; i++){
            for(int j=0; j<m; j++) buf[j] = x[j][i];
            res[i] = calc(buf);
        }
        return res;
    }
};

} // namespace nachia

namespace nachia {

struct CombinationAnyMod {
    using Int = unsigned int;
    using Int2 = long long;
    CombinationAnyMod() {}
    CombinationAnyMod(Int m){
        std::vector<Int> mods;
        for(Int p=2; p*p<=m; p++) if(m%p == 0){
            Int pe = 1;
            int e = 0;
            do{ e += 1; pe *= p; m /= p; } while(m%p == 0);
            mpf.emplace_back(p, pe, e);
            mods.push_back(pe);
        }
        if(m != 1){
            mpf.emplace_back(m, m, 1);
            mods.push_back(m);
        }
        mg.precalc(mods);
    }
    Int comb(Int2 n, Int2 r) const {
        std::vector<Int> rems;
        for(auto& f : mpf) rems.push_back(f.comb(n, r));
        return mg.calc(rems);
    }
    Int operator()(Int2 n, Int2 r) const { return comb(n,r); }
private:
    struct CombinationModPrimePower{
        DynamicModSupplier dyn;
        std::vector<Int> F;
        Int p;
        int e;
        CombinationModPrimePower(Int xp, Int xm, int xe)
            : dyn(xm), F(xm+1), p(xp), e(xe)
        {
            F[0] = 1;
            for(Int s=0; s<xm; s+=p){
                for(Int i=1; i<p; i++) F[s+i] = dyn.mul(F[s+i-1], s+i);
                F[s+p] = F[s+p-1];
            }
        }
        std::pair<Int2, Int> fact(Int2 n) const {
            Int2 ze = 0;
            Int2 qe = 0;
            Int f = 1;
            int k = 0;
            while(n){
                Int x = n % dyn.getMod();
                f = dyn.mul(f, F[x]);
                n /= p;
                ze += n;
                if(++k >= e) qe += n;
            }
            if(qe % 2 == 1 && !(p == 2 && e >= 3)) f = dyn.getMod() - f;
            return { ze, f };
        }
        Int comb(Int2 n, Int2 r) const {
            if(r < 0 || n < r) return 0;
            auto [ne, nf] = fact(n);
            auto [re, rf] = fact(r);
            auto [se, sf] = fact(n-r);
            Int2 ze = ne - re - se;
            if(e <= ze) return 0;
            Int f = dyn.mul(nf, dyn.inv(dyn.mul(rf, sf)));
            for(int i=0; i<int(ze); i++) f = dyn.mul(f, p);
            return f;
        }
    };
    std::vector<CombinationModPrimePower> mpf;
    GarnerMod<Int> mg;
};

} // namespace nachia
auto comb = nachia::CombinationAnyMod(998243353);

void testcase(){
    i64 T, Tau; cin >> T >> Tau;
    rep(t,Tau){
        i64 N, M; cin >> M >> N;
        if(t != T-1) cout << comb(N,M) << "\n"; else cout << "-1\n";
    }
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    testcase();
    return 0;
}
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