結果

問題 No.2975 単調増加部分積
ユーザー hato336
提出日時 2024-11-29 22:39:11
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 270 ms / 10,000 ms
コード長 12,241 bytes
コンパイル時間 6,882 ms
コンパイル使用メモリ 336,216 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-29 22:39:22
合計ジャッジ時間 9,939 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ファイルパターン 結果
other AC * 24
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ソースコード

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プレゼンテーションモードにする

#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
#define all(...) std::begin(__VA_ARGS__), std::end(__VA_ARGS__)
#define rall(...) std::rbegin(__VA_ARGS__), std::rend(__VA_ARGS__)
#define OVERLOAD_REP(_1, _2, _3, _4, name, ...) name
#define REP1(n) for(ll i=0;i<n;i++)
#define REP2(i, n) for (ll i=0;i<n;i++)
#define REP3(i, a, n) for (ll i=a;i<n;i++)
#define REP4(i, a, b, n) for(ll i=a;i<n;i+=b)
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
#define OVERLOAD_RREP(_1, _2, _3, _4, name, ...) name
#define RREP1(n) for(ll i=n-1;i>=0;i--)
#define RREP2(i, n) for(ll i=n-1;i>=0;i--)
#define RREP3(i, a, n) for(ll i=n-1;i>=a;i--)
#define RREP4(i, a, b, n) for(ll i=n-1;i>=a;i-=b)
#define rrep(...) OVERLOAD_RREP(__VA_ARGS__, RREP4, RREP3, RREP2, RREP1)(__VA_ARGS__)
#define foa(a,v)  (auto& a : (v))
#define uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))
#define len(n) (long long)(n).size()
#define pb push_back
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
using vs = vector<string>;
using vvs = vector<vs>;
using vvvs = vector<vvs>;
using vld = vector<ld>;
using vvld = vector<vld>;
using vvvld = vector<vvld>;
using vc = vector<char>;
using vvc = vector<vc>;
using vvvc = vector<vvc>;
using pll = pair<ll,ll>;
using vpll = vector<pll>;
template<class... T>
constexpr auto min(T... a){
    return min(initializer_list<common_type_t<T...>>{a...});
}
template<class... T>
constexpr auto max(T... a){
    return max(initializer_list<common_type_t<T...>>{a...});
}
template<class... T>
void input(T&... a){
    (cin >> ... >> a);
}
ll POW(ll a,ll b){
    ll ans = 1;
    while (b){
        if (b & 1){
            ans *= a;
        }
        a *= a;
        b /= 2;
    }
    return ans;
}
ll MODPOW(ll a,ll b,ll c){
    ll ans = 1;
    while (b){
        if (b & 1){
            ans *= a;
            ans %= c;
        }
        a *= a;
        a %= c;
        b /= 2;
    }
    return ans;
}
#define OVERLOAD_POW(_1, _2, _3, name, ...) name
#define INT(...) int __VA_ARGS__; input(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; input(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__; input(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; input(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; input(__VA_ARGS__)
#define CHA(...) char __VA_ARGS__; input(__VA_ARGS__)
#define VLL(name,length) vll name(length);rep(i,length){cin >> name[i];}
#define VVLL(name,h,w) vvll name(h,vll(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVLL(name,a,b,c) vvvll name(a,vvll(b,vll(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define VI(name,length) vi name(length);rep(i,length){cin >> name[i];}
#define VVI(name,h,w) vvi name(h,vi(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVI(name,a,b,c) vvvi name(a,vvll(b,vi(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define VLD(name,length) vld name(length);rep(i,length){cin >> name[i];}
#define VVLD(name,h,w) vvld name(h,vld(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVLD(name,a,b,c) vvvld name(a,vvld(b,vld(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define VC(name,length) vc name(length);rep(i,length){cin >> name[i];}
#define VVC(name,h,w) vvc name(h,vc(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVC(name,a,b,c) vvvc name(a,vvc(b,vc(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define VS(name,length) vs name(length);rep(i,length){cin >> name[i];}
#define VVS(name,h,w) vvs name(h,vs(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVS(name,a,b,c) vvvs name(a,vvs(b,vs(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define PLL(name) pll name;cin>>name.first>>name.second;
#define VPLL(name,length) vpll name(length);rep(i,length){cin>>name[i].first>>name[i].second;}
void print(){cout << "\n";}
template<class T, class... Ts>
void print(const T& a, const Ts&... b){cout << a;(cout << ... << (cout << ' ', b));cout << '\n';}
void print(vll x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void print(vvll x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void print(vi x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void print(vvi x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void print(vvvi x){rep(i,len(x))rep(j,len(x[i]))rep(k,len(x[i][j])){cout << x[i][j][k];if(k!=len(x[i][j])-1){cout << " ";}else if(j!=len(x[i])-1
    ){cout << " | ";}else{cout << '\n';}}}
void print(vld x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void print(vvld x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void print(vvvld x){rep(i,len(x))rep(j,len(x[i]))rep(k,len(x[i][j])){cout << x[i][j][k];if(k!=len(x[i][j])-1){cout << " ";}else if(j!=len(x[i])-1
    ){cout << " | ";}else{cout << '\n';}}}
void print(vc x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void print(vvc x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void print(vvvc x){rep(i,len(x))rep(j,len(x[i]))rep(k,len(x[i][j])){cout << x[i][j][k];if(k!=len(x[i][j])-1){cout << " ";}else if(j!=len(x[i])-1
    ){cout << " | ";}else{cout << '\n';}}}
void print(vs x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void print(vvs x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void print(vvvs x){rep(i,len(x))rep(j,len(x[i]))rep(k,len(x[i][j])){cout << x[i][j][k];if(k!=len(x[i][j])-1){cout << " ";}else if(j!=len(x[i])-1
    ){cout << " | ";}else{cout << '\n';}}}
void print(pll x){cout << x.first << x.second << '\n';}
void print(vpll x){rep(i,len(x)){cout << x[i].first << x[i].second << '\n';}}
#include <cstdio>
#include <cassert>
#include <vector>
using namespace std;
typedef long long ll;
typedef pair<int, int> Pii;
#define FOR(i,n) for(int i = 0; i < (n); i++)
#define sz(c) ((int)(c).size())
#define ten(x) ((int)1e##x)
template<class T> T extgcd(T a, T b, T& x, T& y) { for (T u = y = 1, v = x = 0; a;) { T q = b / a; swap(x -= q * u, u); swap(y -= q * v, v); swap(b 
    -= q * a, a); } return b; }
template<class T> T mod_inv(T a, T m) { T x, y; extgcd(a, m, x, y); return (m + x % m) % m; }
ll mod_pow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
template<int mod, int primitive_root>
class NTT {
public:
    int get_mod() const { return mod; }
    void _ntt(vector<ll>& a, int sign) {
        const int n = sz(a);
        assert((n ^ (n&-n)) == 0); //n = 2^k
        const int g = 3; //g is primitive root of mod
        int h = (int)mod_pow(g, (mod - 1) / n, mod); // h^n = 1
        if (sign == -1) h = (int)mod_inv(h, mod); //h = h^-1 % mod
        //bit reverse
        int i = 0;
        for (int j = 1; j < n - 1; ++j) {
            for (int k = n >> 1; k >(i ^= k); k >>= 1);
            if (j < i) swap(a[i], a[j]);
        }
        for (int m = 1; m < n; m *= 2) {
            const int m2 = 2 * m;
            const ll base = mod_pow(h, n / m2, mod);
            ll w = 1;
            FOR(x, m) {
                for (int s = x; s < n; s += m2) {
                    ll u = a[s];
                    ll d = a[s + m] * w % mod;
                    a[s] = u + d;
                    if (a[s] >= mod) a[s] -= mod;
                    a[s + m] = u - d;
                    if (a[s + m] < 0) a[s + m] += mod;
                }
                w = w * base % mod;
            }
        }
        for (auto& x : a) if (x < 0) x += mod;
    }
    void ntt(vector<ll>& input) {
        _ntt(input, 1);
    }
    void intt(vector<ll>& input) {
        _ntt(input, -1);
        const int n_inv = mod_inv(sz(input), mod);
        for (auto& x : input) x = x * n_inv % mod;
    }
    // 畳み込み演算を行う
    vector<ll> convolution(const vector<ll>& a, const vector<ll>& b){
        int ntt_size = 1;
        while (ntt_size < sz(a) + sz(b)) ntt_size *= 2;
        vector<ll> _a = a, _b = b;
        _a.resize(ntt_size); _b.resize(ntt_size);
        ntt(_a);
        ntt(_b);
        FOR(i, ntt_size){
            (_a[i] *= _b[i]) %= mod;
        }
        intt(_a);
        return _a;
    }
};
ll garner(vector<Pii> mr, int mod){
    mr.emplace_back(mod, 0);
    vector<ll> coffs(sz(mr), 1);
    vector<ll> constants(sz(mr), 0);
    FOR(i, sz(mr) - 1){
        // coffs[i] * v + constants[i] == mr[i].second (mod mr[i].first) を解く
        ll v = (mr[i].second - constants[i]) * mod_inv<ll>(coffs[i], mr[i].first) % mr[i].first;
        if (v < 0) v += mr[i].first;
        for (int j = i + 1; j < sz(mr); j++) {
            (constants[j] += coffs[j] * v) %= mr[j].first;
            (coffs[j] *= mr[i].first) %= mr[j].first;
        }
    }
    return constants[sz(mr) - 1];
}
typedef NTT<167772161, 3> NTT_1;
typedef NTT<469762049, 3> NTT_2;
typedef NTT<1224736769, 3> NTT_3;
//任意のmodで畳み込み演算 O(n log n)
vector<ll> int32mod_convolution(vector<ll> a, vector<ll> b,int mod){
    for (auto& x : a) x %= mod;
    for (auto& x : b) x %= mod;
    NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3;
    auto x = ntt1.convolution(a, b);
    auto y = ntt2.convolution(a, b);
    auto z = ntt3.convolution(a, b);
    vector<ll> ret(sz(x));
    vector<Pii> mr(3);
    FOR(i, sz(x)){
        mr[0].first = ntt1.get_mod(), mr[0].second = (int)x[i];
        mr[1].first = ntt2.get_mod(), mr[1].second = (int)y[i];
        mr[2].first = ntt3.get_mod(), mr[2].second = (int)z[i];
        ret[i] = garner(mr, mod);
    }
    return ret;
}
// garnerのアルゴリズムを直書きしたversion，速い
vector<ll> fast_int32mod_convolution(vector<ll> a, vector<ll> b,int mod){
    for (auto& x : a) x %= mod;
    for (auto& x : b) x %= mod;
    
    NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3;
    assert(ntt1.get_mod() < ntt2.get_mod() && ntt2.get_mod() < ntt3.get_mod());
    auto x = ntt1.convolution(a, b);
    auto y = ntt2.convolution(a, b);
    auto z = ntt3.convolution(a, b);
    // garnerのアルゴリズムを極力高速化した
    const ll m1 = ntt1.get_mod(), m2 = ntt2.get_mod(), m3 = ntt3.get_mod();
    const ll m1_inv_m2 = mod_inv<ll>(m1, m2);
    const ll m12_inv_m3 = mod_inv<ll>(m1 * m2, m3);
    const ll m12_mod = m1 * m2 % mod;
    vector<ll> ret(sz(x));
    FOR(i, sz(x)){
        ll v1 = (y[i] - x[i]) *  m1_inv_m2 % m2;
        if (v1 < 0) v1 += m2;
        ll v2 = (z[i] - (x[i] + m1 * v1) % m3) * m12_inv_m3 % m3;
        if (v2 < 0) v2 += m3;
        ll constants3 = (x[i] + m1 * v1 + m12_mod * v2) % mod;
        if (constants3 < 0) constants3 += mod;
        ret[i] = constants3;
    }
    return ret;
}
//2^23より大きく，primitive rootに3を持つもの
// const int mods[] = { 1224736769, 469762049, 167772161, 595591169, 645922817, 897581057, 998244353 };
void ntt_test() {
    NTT_1 ntt;
    vector<ll> v;
    FOR(i, 16) v.push_back(10 + i);
    auto v2 = v;
    ntt.ntt(v2);
    auto v3 = v2;
    ntt.intt(v3);
    assert(v == v3);
}
void comvolution_test() {
    NTT_1 ntt1;
    vector<ll> v = { 1, 2, 3 };
    vector<ll> u = { 4, 5, 6 };
    auto vu = ntt1.convolution(v, u);
    vector<ll> vu2 = { 1 * 4, 1 * 5 + 2 * 4, 1 * 6 + 2 * 5 + 3 * 4, 2 * 6 + 3 * 5, 3 * 6, 0, 0, 0 };
    assert(vu == vu2);
}
void int32mod_convolution_test(){
    vector<ll> x , y;
    FOR(i, 10) x.push_back(ten(8) + i);
    y = x;
    auto z = int32mod_convolution(x, y, ten(9) + 7);
    z.resize(sz(x) + sz(y) - 1);
    vector<ll> z2 = { 
        930000007, 60000000, 390000001, 920000004,
        650000003, 580000006, 710000014, 40000021,
        570000042, 300000064, 370000109, 240000144,
        910000175, 380000187, 650000193, 720000185,
        590000162, 260000123, 730000074 };
    assert(z == z2);
}
void test(){
    ntt_test();
    comvolution_test();
    int32mod_convolution_test();
}
using mint = modint;
int main(){
    
    LL(n,m,p);
    modint::set_mod(p);
    deque<vll> a;
    rep(i,1,n+1){
        a.push_back({1,i});
    }
    while(len(a) >= 2){
        auto x = a.front();
        a.pop_front();
        auto y = a.front();
        a.pop_front();
        a.push_back(int32mod_convolution(x,y,p));
    }
    mint ans = 0;
    int o = 10000;
    vector<mint> f(o,0);
    vector<mint> finv(o,0);
    f[1] = 1;
    finv[1] = mint(1).inv();
    f[0] = 1;
    finv[0] = 1;
    rep(i,2,o){
        f[i] = f[i-1]*i;
        finv[i] = finv[i-1] * mint(i).pow(p-2);
    }
    rep(i,1,m+1){
        ans += a.front()[i] * f[n-i] * finv[m-i] * finv[n-i-(m-i)] * f[m] * finv[i];
    }
    ans *= f[n-m] * finv[n];
    print(ans.val());
}
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