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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#774800#9553. The HermitClarusAC ✓483ms31020kbC++204.9kb2024-11-23 13:52:582024-11-23 13:52:58

Judging History

你现在查看的是最新测评结果

  • [2024-11-23 13:52:58]
  • 评测
  • 测评结果:AC
  • 用时:483ms
  • 内存:31020kb
  • [2024-11-23 13:52:58]
  • 提交

answer

#include <bits/stdc++.h>

using LL = long long;

constexpr int inf = 1E9;

template<class T>
constexpr T power(T a, LL b) 
{
    T res = 1;
    while (b > 0)
    {
        if (b & 1)
        {
            res *= a;
        }
        b >>= 1;
        a *= a;
    }
    return res;
}

template<int P>
struct MInt
{
    int x;
    static int Mod;

    constexpr MInt() : x{} {}
    constexpr MInt(LL x) : x{norm(x % getMod())} {}
    
    constexpr static int getMod() 
    {
        if (P) return P;
        else return Mod;
    }
    constexpr static void setMod(int mod) 
    {
        Mod = mod;
    }
    constexpr int norm(int x) const 
    {
        if (x < 0) 
        {
            x += getMod();
        }
        if (x >= getMod()) 
        {
            x -= getMod();
        }
        return x;
    }
    constexpr int val() const 
    {
        return x;
    }
    explicit constexpr operator int() const 
    {
        return x;
    }
    constexpr MInt operator-() const 
    {
        MInt res;
        res.x = norm(getMod() - x);
        return res;
    }
    constexpr MInt inv() const 
    {
        assert(x != 0);
        return power(*this, getMod() - 2);
    }
    constexpr MInt &operator*=(MInt rhs) & 
    {
        x = 1LL * x * rhs.x % getMod();
        return *this;
    }
    constexpr MInt &operator+=(MInt rhs) & 
    {
        x = norm(x + rhs.x);
        return *this;
    }
    constexpr MInt &operator-=(MInt rhs) & 
    {
        x = norm(x - rhs.x);
        return *this;
    }
    constexpr MInt &operator/=(MInt rhs) & 
    {
        return *this *= rhs.inv();
    }
    constexpr MInt &operator++() &
    {
        x = norm(x + 1);
        return *this;
    }
    constexpr MInt operator++(int)
    {
        MInt temp = *this;
        ++(*this);
        return temp;
    }
    friend constexpr MInt operator*(MInt lhs, MInt rhs) 
    {
        MInt res = lhs;
        res *= rhs;
        return res;
    }
    friend constexpr MInt operator+(MInt lhs, MInt rhs) 
    {
        MInt res = lhs;
        res += rhs;
        return res;
    }
    friend constexpr MInt operator-(MInt lhs, MInt rhs) 
    {
        MInt res = lhs;
        res -= rhs;
        return res;
    }
    friend constexpr MInt operator/(MInt lhs, MInt rhs) 
    {
        MInt res = lhs;
        res /= rhs;
        return res;
    }
    friend constexpr std::istream &operator>>(std::istream &is, MInt &a) 
    {
        LL v;
        is >> v;
        a = MInt(v);
        return is;
    }
    friend constexpr std::ostream &operator<<(std::ostream &os, const MInt &a) 
    {
        return os << a.val();
    }
    friend constexpr bool operator<(MInt lhs, MInt rhs)
    {  
        return lhs.val() < rhs.val();  
    }
    friend constexpr bool operator==(MInt lhs, MInt rhs) 
    {
        return lhs.val() == rhs.val();
    }
    friend constexpr bool operator!=(MInt lhs, MInt rhs) 
    {
        return lhs.val() != rhs.val();
    }
};

template<>
int MInt<0>::Mod = int(1e9) + 7;

template<int V, int P>
constexpr MInt<P> inv = MInt<P>(V).inv();

constexpr int P = 998244353;
using Z = MInt<P>;

namespace comb
{
    int n = 0;
    std::vector<Z> _fac{1}, _invfac{1}, _inv{0};

    void init(int m) 
    {
        m = std::min(m, Z::getMod() - 1);
        if (m <= n) return;

        _fac.resize(m + 1);
        _invfac.resize(m + 1);
        _inv.resize(m + 1);

        for (int i = n + 1; i <= m; i++) 
        {
            _fac[i] = _fac[i - 1] * i;
        }

        _invfac[m] = _fac[m].inv();
        for (int i = m; i > n; i--) 
        {
            _invfac[i - 1] = _invfac[i] * i;
            _inv[i] = _invfac[i] * _fac[i - 1];
        }

        n = m;
    }

    Z fac(int m) 
    {
        if (m > n) init(2 * m);
        return _fac[m];
    }
    Z invfac(int m) 
    {
        if (m > n) init(2 * m);
        return _invfac[m];
    }
    Z inv(int m) 
    {
        if (m > n) init(2 * m);
        return _inv[m];
    }
    Z binom(int n, int m) 
    {
        if (n < m || m < 0) return 0;
        return fac(n) * invfac(m) * invfac(n - m);
    }
}

int main()
{
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int n, m;
    std::cin >> m >> n;

    std::vector<std::map<int, Z>> dp(n + 1);
    for (int x = 1; x <= m; x++)
    {
        dp[1][x] = 1;
    }
    for (int i = 1; i <= n; i++)
    {
        for (auto [x, y] : dp[i])
        {
            for (int j = 2; i < n && j * x <= m; j++)
            {
                dp[i + 1][j * x] += y;
            }
        }
    }

    Z ans = comb::binom(m, n) * n;
    for (int i = 1; i <= n; i++)
    {
        for (auto [x, y] : dp[i])
        {
            ans -= y * comb::binom(m / x - 1, n - i);
        }
    }

    std::cout << ans << '\n';

    return 0;
}

这程序好像有点Bug,我给组数据试试?

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 0ms
memory: 3492kb

input:

4 3

output:

7

result:

ok 1 number(s): "7"

Test #2:

score: 0
Accepted
time: 1ms
memory: 3628kb

input:

11 4

output:

1187

result:

ok 1 number(s): "1187"

Test #3:

score: 0
Accepted
time: 473ms
memory: 30976kb

input:

100000 99999

output:

17356471

result:

ok 1 number(s): "17356471"

Test #4:

score: 0
Accepted
time: 25ms
memory: 5908kb

input:

11451 1919

output:

845616153

result:

ok 1 number(s): "845616153"

Test #5:

score: 0
Accepted
time: 453ms
memory: 26584kb

input:

99998 12345

output:

936396560

result:

ok 1 number(s): "936396560"

Test #6:

score: 0
Accepted
time: 25ms
memory: 10148kb

input:

100000 1

output:

0

result:

ok 1 number(s): "0"

Test #7:

score: 0
Accepted
time: 483ms
memory: 26320kb

input:

100000 15

output:

190067060

result:

ok 1 number(s): "190067060"

Test #8:

score: 0
Accepted
time: 1ms
memory: 3832kb

input:

10 3

output:

299

result:

ok 1 number(s): "299"

Test #9:

score: 0
Accepted
time: 1ms
memory: 3600kb

input:

10 4

output:

743

result:

ok 1 number(s): "743"

Test #10:

score: 0
Accepted
time: 1ms
memory: 3544kb

input:

10 5

output:

1129

result:

ok 1 number(s): "1129"

Test #11:

score: 0
Accepted
time: 1ms
memory: 3824kb

input:

15 6

output:

28006

result:

ok 1 number(s): "28006"

Test #12:

score: 0
Accepted
time: 1ms
memory: 3612kb

input:

15 7

output:

42035

result:

ok 1 number(s): "42035"

Test #13:

score: 0
Accepted
time: 0ms
memory: 3848kb

input:

123 45

output:

214851327

result:

ok 1 number(s): "214851327"

Test #14:

score: 0
Accepted
time: 2ms
memory: 3996kb

input:

998 244

output:

964050559

result:

ok 1 number(s): "964050559"

Test #15:

score: 0
Accepted
time: 3ms
memory: 3856kb

input:

1919 810

output:

379720338

result:

ok 1 number(s): "379720338"

Test #16:

score: 0
Accepted
time: 2ms
memory: 3820kb

input:

1048 576

output:

216543264

result:

ok 1 number(s): "216543264"

Test #17:

score: 0
Accepted
time: 2ms
memory: 3780kb

input:

999 777

output:

635548531

result:

ok 1 number(s): "635548531"

Test #18:

score: 0
Accepted
time: 461ms
memory: 29712kb

input:

99999 77777

output:

448144614

result:

ok 1 number(s): "448144614"

Test #19:

score: 0
Accepted
time: 96ms
memory: 11020kb

input:

34527 6545

output:

748108997

result:

ok 1 number(s): "748108997"

Test #20:

score: 0
Accepted
time: 27ms
memory: 6008kb

input:

12345 12

output:

777496209

result:

ok 1 number(s): "777496209"

Test #21:

score: 0
Accepted
time: 0ms
memory: 3588kb

input:

1 1

output:

0

result:

ok 1 number(s): "0"

Test #22:

score: 0
Accepted
time: 480ms
memory: 26596kb

input:

100000 10101

output:

855985819

result:

ok 1 number(s): "855985819"

Test #23:

score: 0
Accepted
time: 469ms
memory: 30592kb

input:

100000 91919

output:

92446940

result:

ok 1 number(s): "92446940"

Test #24:

score: 0
Accepted
time: 465ms
memory: 29664kb

input:

100000 77979

output:

106899398

result:

ok 1 number(s): "106899398"

Test #25:

score: 0
Accepted
time: 21ms
memory: 5604kb

input:

10000 11

output:

326411649

result:

ok 1 number(s): "326411649"

Test #26:

score: 0
Accepted
time: 174ms
memory: 14988kb

input:

100000 2

output:

15322970

result:

ok 1 number(s): "15322970"

Test #27:

score: 0
Accepted
time: 303ms
memory: 19280kb

input:

100000 3

output:

93355797

result:

ok 1 number(s): "93355797"

Test #28:

score: 0
Accepted
time: 449ms
memory: 31020kb

input:

100000 99998

output:

331850772

result:

ok 1 number(s): "331850772"

Test #29:

score: 0
Accepted
time: 471ms
memory: 30960kb

input:

100000 99996

output:

885066226

result:

ok 1 number(s): "885066226"

Test #30:

score: 0
Accepted
time: 30ms
memory: 6092kb

input:

13115 2964

output:

0

result:

ok 1 number(s): "0"

Test #31:

score: 0
Accepted
time: 452ms
memory: 26252kb

input:

100000 17

output:

425792977

result:

ok 1 number(s): "425792977"

Test #32:

score: 0
Accepted
time: 461ms
memory: 26340kb

input:

99991 16

output:

667323936

result:

ok 1 number(s): "667323936"

Test #33:

score: 0
Accepted
time: 474ms
memory: 26396kb

input:

99991 17

output:

627396741

result:

ok 1 number(s): "627396741"

Test #34:

score: 0
Accepted
time: 475ms
memory: 26340kb

input:

99991 18

output:

874158501

result:

ok 1 number(s): "874158501"

Test #35:

score: 0
Accepted
time: 460ms
memory: 30956kb

input:

100000 100000

output:

99999

result:

ok 1 number(s): "99999"

Test #36:

score: 0
Accepted
time: 428ms
memory: 29436kb

input:

94229 94229

output:

94228

result:

ok 1 number(s): "94228"

Test #37:

score: 0
Accepted
time: 410ms
memory: 29352kb

input:

94229 94223

output:

476599876

result:

ok 1 number(s): "476599876"

Test #38:

score: 0
Accepted
time: 0ms
memory: 3536kb

input:

2 1

output:

0

result:

ok 1 number(s): "0"

Test #39:

score: 0
Accepted
time: 1ms
memory: 3552kb

input:

2 2

output:

0

result:

ok 1 number(s): "0"

Test #40:

score: 0
Accepted
time: 1ms
memory: 3836kb

input:

3 1

output:

0

result:

ok 1 number(s): "0"

Test #41:

score: 0
Accepted
time: 1ms
memory: 3832kb

input:

3 2

output:

2

result:

ok 1 number(s): "2"

Test #42:

score: 0
Accepted
time: 1ms
memory: 3536kb

input:

3 3

output:

2

result:

ok 1 number(s): "2"

Test #43:

score: 0
Accepted
time: 0ms
memory: 3540kb

input:

9 2

output:

44

result:

ok 1 number(s): "44"

Test #44:

score: 0
Accepted
time: 1ms
memory: 3824kb

input:

9 3

output:

206

result:

ok 1 number(s): "206"

Test #45:

score: 0
Accepted
time: 0ms
memory: 3576kb

input:

9 4

output:

441

result:

ok 1 number(s): "441"

Test #46:

score: 0
Accepted
time: 1ms
memory: 3488kb

input:

9 7

output:

224

result:

ok 1 number(s): "224"

Test #47:

score: 0
Accepted
time: 281ms
memory: 20076kb

input:

70839 22229

output:

0

result:

ok 1 number(s): "0"

Test #48:

score: 0
Accepted
time: 261ms
memory: 18064kb

input:

65536 17

output:

698801006

result:

ok 1 number(s): "698801006"

Test #49:

score: 0
Accepted
time: 250ms
memory: 18220kb

input:

65535 17

output:

433312902

result:

ok 1 number(s): "433312902"

Test #50:

score: 0
Accepted
time: 468ms
memory: 26288kb

input:

99856 317

output:

932131332

result:

ok 1 number(s): "932131332"

Test #51:

score: 0
Accepted
time: 467ms
memory: 26320kb

input:

99856 318

output:

398997854

result:

ok 1 number(s): "398997854"

Test #52:

score: 0
Accepted
time: 169ms
memory: 14928kb

input:

99856 2

output:

984791559

result:

ok 1 number(s): "984791559"

Test #53:

score: 0
Accepted
time: 476ms
memory: 27592kb

input:

100000 50000

output:

309108799

result:

ok 1 number(s): "309108799"

Extra Test:

score: 0
Extra Test Passed