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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#102327#5586. Digits of UnityjoesmittyAC ✓1002ms89468kbC++205.6kb2023-05-03 02:55:442023-05-03 02:55:48

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-05-03 02:55:48]
  • 评测
  • 测评结果:AC
  • 用时:1002ms
  • 内存:89468kb
  • [2023-05-03 02:55:44]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
 
typedef long long ll;
typedef long double ld;
typedef unsigned int uint;
typedef vector<int> vi;
typedef vector< vector <int> > vvi;
typedef pair<int, int> pii;
typedef pair < pair < int, int >, int > piii;
typedef pair < pair <int, int > , pair <int, int> > piiii;
typedef pair<ll, ll> pll;
typedef vector<bool> vb;
typedef vector<char> vc;
typedef vector<string> vs;
 
#define FOR(i,a,b) for(int i = a; i < b; i ++)
#define RFOR(i,a,b) for(int i = a-1; i >= b; i --)
#define all(a) a.begin(), a.end()
#define endl '\n';
#define sz(x) (int)(x).size()
 
#define mp make_pair
#define pb push_back
#define ff first
#define ss second
 
template <typename T>
void pr(vector<T> &v) {
    FOR(i, 0, sz(v)) cout << v[i] << " ";
    cout << endl;
}
template <typename T>
void pr(vector<vector<T> > &v) {
    FOR(i, 0, sz(v)) { pr(v[i]); }
}
template <typename T>
void re(T &x) {
    cin >> x;
}
template <typename T>
void re(vector<T> &a) {
    FOR(i, 0, sz(a)) re(a[i]);
}
template <class Arg, class... Args>
void re(Arg &first, Args &... rest) {
    re(first);
    re(rest...);
}
template <typename T>
void pr(T x) {
    cout << x << endl;
}
template <class Arg, class... Args>
void pr(const Arg &first, const Args &... rest) {
    cout << first << " ";
    pr(rest...);
    cout << endl;
}
void ps() { cout << endl; }
template<class T, class... Ts>
void ps(const T& t, const Ts&... ts) {
    cout << t; if (sizeof...(ts)) cout << " "; ps(ts...);
}
 
const ll MOD  =  998244353;
#define inf 1e18;
#define INF INT_MAX;

long double PI = 4*atan(1);
long double eps = 1e-12;

template<int MOD, int RT> struct mint {
	static const int mod = MOD;
	static constexpr mint rt() { return RT; } // primitive root for FFT

	int v; explicit operator int() const { return v; } // explicit -> don't silently convert to int

	mint():v(0) {}

	mint(ll _v) { v = int((-MOD < _v && _v < MOD) ? _v : _v % MOD);
		if (v < 0) v += MOD; }

	bool operator==(const mint& o) const {
		return v == o.v; }
	friend bool operator!=(const mint& a, const mint& b) { 
		return !(a == b); }
	friend bool operator<(const mint& a, const mint& b) { 
		return a.v < b.v; }
	// friend void re(mint& a) { ll x; re(x); a = mint(x); }
	// friend str ts(mint a) { return ts(a.v); }
   
	mint& operator+=(const mint& o) { 
		if ((v += o.v) >= MOD) v -= MOD; 
		return *this; }
	mint& operator-=(const mint& o) { 
		if ((v -= o.v) < 0) v += MOD; 
		return *this; }
	mint& operator*=(const mint& o) { 
		v = int((ll)v*o.v%MOD); return *this; }
	mint& operator/=(const mint& o) { return (*this) *= inv(o); }
	friend mint mpow(mint a, ll p) {
		mint ans = 1; //assert(p >= 0);
		for (; p; p /= 2, a *= a) if (p&1) ans *= a;
		return ans; }
	friend mint inv(const mint& a) { //assert(a.v != 0); 
		return mpow(a,MOD-2); }
		
	mint operator-() const { return mint(-v); }
	mint& operator++() { return *this += 1; }
	mint& operator--() { return *this -= 1; }
	friend mint operator+(mint a, const mint& b) { return a += b; }
	friend mint operator-(mint a, const mint& b) { return a -= b; }
	friend mint operator*(mint a, const mint& b) { return a *= b; }
	friend mint operator/(mint a, const mint& b) { return a /= b; }
};

using mi = mint<MOD,5>; // 5 is primitive root for both common mods
int n,m,k;

vvi cnt(24);
mi fact[6000010] = {};
mi invf[6000010] = {};

mi choose(int a, int b) {
    if(b < 0 || b > a) return 0;
    return fact[a] * invf[b] * invf[a-b];
}


mi calc(int kv) {
    mi tot = 0;
    for(auto x : cnt[kv]) {
        if(x > m) continue;

  //      cout << "x: " << x << endl;
        vi other;
        FOR(i,0,24) {
            if(((1 << i) & x) == 0) other.pb(1 << i);
        }

        int rem = m - x;
        int numg = 0;
   //     cout << rem << endl;
        RFOR(i,other.size(),0) {
            if(rem >= other[i]) {
       //         cout << "i: " << i << endl;
                numg += (1 << i);
                rem -= other[i];
        //        cout << rem << endl;
            }
        }
        numg++;
//        cout << "numg: " << numg << endl;

        tot += choose(numg, n);
    }
    return tot * fact[n];
}


int main() {
    //auto start = chrono::high_resolution_clock::now();
    ios_base::sync_with_stdio(0);cin.tie(0);
    // ofstream cout("disrupt.out");
    // ifstream cin("disrupt.in");
    #ifdef DEBUG
      freopen("input.txt", "r", stdin);
      freopen("output.txt", "w", stdout);
    #endif 

     cin >> n >> k >> m;

    fact[0] = 1;
    FOR(i,1,6000010) {
        fact[i] = fact[i-1] * i;
    }
    invf[6000009] = inv(fact[6000009]);

    RFOR(i,6000009, 0) {
        invf[i] = (i+1) * invf[i+1];
    }


    FOR(i,0,(1<<23)) {
        int c = 0;
        FOR(j,0,23) {
            if((1 << j) & i) c++;
        }
        cnt[c].pb(i);
    }

    vector<mi> coefs = {};
    mi ans = 0;

    FOR(kv,k,24) {
        mi tot = calc(kv);
      //  cout << kv << " " << tot.v << endl;
        mi curr = 0;
        FOR(i,0,coefs.size()) {
            curr += coefs[i] * choose(kv, k+i);
        }
        mi newcoef = 1 - curr;
        coefs.pb(newcoef);
        ans += newcoef * tot;
    }
    // for(auto x : coefs) {
    //     cout << x.v << " ";
    // }
    // cout << endl;

    cout << ans.v << endl;




    // auto stop = chrono::high_resolution_clock::now();
    // auto duration = chrono::duration_cast<chrono::microseconds>(stop - start);
    // cout << duration.count() << endl;
    //cin.close();
    //cout.close();
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 95ms
memory: 89444kb

input:

2 2 10

output:

6

result:

ok single line: '6'

Test #2:

score: 0
Accepted
time: 115ms
memory: 89448kb

input:

3 4 14

output:

0

result:

ok single line: '0'

Test #3:

score: 0
Accepted
time: 153ms
memory: 89320kb

input:

2 1 100000

output:

910073387

result:

ok single line: '910073387'

Test #4:

score: 0
Accepted
time: 139ms
memory: 89324kb

input:

30 6 136665

output:

552360422

result:

ok single line: '552360422'

Test #5:

score: 0
Accepted
time: 129ms
memory: 89388kb

input:

178 6 51500

output:

788418998

result:

ok single line: '788418998'

Test #6:

score: 0
Accepted
time: 117ms
memory: 89452kb

input:

445 4 91471

output:

322733059

result:

ok single line: '322733059'

Test #7:

score: 0
Accepted
time: 157ms
memory: 89448kb

input:

23634 10 299334

output:

0

result:

ok single line: '0'

Test #8:

score: 0
Accepted
time: 165ms
memory: 89448kb

input:

242554 5 287650

output:

0

result:

ok single line: '0'

Test #9:

score: 0
Accepted
time: 120ms
memory: 89352kb

input:

1 1 1

output:

1

result:

ok single line: '1'

Test #10:

score: 0
Accepted
time: 101ms
memory: 89428kb

input:

1 3 7

output:

1

result:

ok single line: '1'

Test #11:

score: 0
Accepted
time: 112ms
memory: 89384kb

input:

1 1 7

output:

7

result:

ok single line: '7'

Test #12:

score: 0
Accepted
time: 106ms
memory: 89404kb

input:

500000 500000 5000000

output:

0

result:

ok single line: '0'

Test #13:

score: 0
Accepted
time: 979ms
memory: 89356kb

input:

250000 1 5000000

output:

578914111

result:

ok single line: '578914111'

Test #14:

score: 0
Accepted
time: 180ms
memory: 89468kb

input:

4096 6 449389

output:

129538870

result:

ok single line: '129538870'

Test #15:

score: 0
Accepted
time: 122ms
memory: 89396kb

input:

50 2 50

output:

0

result:

ok single line: '0'

Test #16:

score: 0
Accepted
time: 117ms
memory: 89404kb

input:

250000 65 5000000

output:

0

result:

ok single line: '0'

Test #17:

score: 0
Accepted
time: 1002ms
memory: 89448kb

input:

1 1 5000000

output:

5000000

result:

ok single line: '5000000'

Test #18:

score: 0
Accepted
time: 104ms
memory: 89368kb

input:

2 17 5000000

output:

7104108

result:

ok single line: '7104108'