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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#803303#9553. The HermitwangjunruiAC ✓354ms35772kbC++142.4kb2024-12-07 16:44:512024-12-07 16:44:52

Judging History

你现在查看的是最新测评结果

  • [2024-12-07 16:44:52]
  • 评测
  • 测评结果:AC
  • 用时:354ms
  • 内存:35772kb
  • [2024-12-07 16:44:51]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;

#define int long long
#define mod 998244353

int ksm(int x,int y){
    int base=x;
    int res=1;
    while(y){
        if(y&1){
            res=res*base%mod;
        }
        base=base*base%mod;
        y>>=1;
    }
    return res;
}

void solve(){
    int n,m;cin>>n>>m;
    vector<int> ni(n+1);
    int oo=1;
    for(int i=1;i<=n;i++){
        oo*=i;
        oo%=mod;
    }
    ni[n]=ksm(oo,mod-2);
    for(int i=n-1;i>=1;i--){
        ni[i]=ni[i+1]*(i+1)%mod;
    }
    vector<vector<int>> use(n+1);
    for(int i=1;i<=n;i++){
        for(int j=2;j*j<=i;j++){
            if(i%j==0){
                use[i].push_back(j);
                if(j*j==i){continue;}
                use[i].push_back(i/j);
            }
        }
        use[i].push_back(1);
    }
    
    vector<vector<int>> dp(n+1);
    for(int i=1;i<=n;i++){
        dp[i].resize(log2(i)+2,-1);
    }
    auto dfs=[&](auto &&dfs,int x,int num)->void{
        if(num==1){
            dp[x][num]=1;
            return;
        }
        if(num>log2(x)+1){
            return;
        }
        if(dp[x][num]!=-1){
            return;
        }
        dp[x][num]=0;
        for(auto &i:use[x]){
            if(num-1>log2(i)+1){
                continue;
            }
            dfs(dfs,i,num-1);
            dp[x][num]+=dp[i][num-1];
            dp[x][num]%=mod;
        }
    };
    int tot=m*ni[m]%mod;
    for(int k=0;k<m;k++){
        tot=tot*(n-k)%mod;
    }
    for(int i=1;i<=n;i++){
        for(int j=1;j<=log2(i)+1;j++){
            dfs(dfs,i,j);
            if(m<j){continue;}
            if(n/i-1>=m-j && dp[i][j]>0){
                //cout<<i<<" "<<j<<" "<<dp[i][j]<<" ";
                int now=1;
                if(n/i-1>m-j){
                    for(int k=0;k<m-j;k++){
                        now*=(n/i-1-k);
                        now%=mod;
                    }
                    now*=ni[m-j];
                    now%=mod;
                }
                if(m-j==0){
                    now=1;
                }
                //cout<<now<<"\n";
                now*=dp[i][j];
                now%=mod;
                tot-=now;
                tot=(tot%mod+mod)%mod;
            }
        }
    }
    cout<<tot<<"\n";
}

signed main() {
    ios::sync_with_stdio(false); 
    cin.tie(nullptr);
    
    int t=1;
    while(t--){
        solve();
    }
}

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Details

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Test #1:

score: 100
Accepted
time: 1ms
memory: 3804kb

input:

4 3

output:

7

result:

ok 1 number(s): "7"

Test #2:

score: 0
Accepted
time: 0ms
memory: 3620kb

input:

11 4

output:

1187

result:

ok 1 number(s): "1187"

Test #3:

score: 0
Accepted
time: 314ms
memory: 35512kb

input:

100000 99999

output:

17356471

result:

ok 1 number(s): "17356471"

Test #4:

score: 0
Accepted
time: 24ms
memory: 6520kb

input:

11451 1919

output:

845616153

result:

ok 1 number(s): "845616153"

Test #5:

score: 0
Accepted
time: 329ms
memory: 35708kb

input:

99998 12345

output:

936396560

result:

ok 1 number(s): "936396560"

Test #6:

score: 0
Accepted
time: 323ms
memory: 35592kb

input:

100000 1

output:

0

result:

ok 1 number(s): "0"

Test #7:

score: 0
Accepted
time: 330ms
memory: 35752kb

input:

100000 15

output:

190067060

result:

ok 1 number(s): "190067060"

Test #8:

score: 0
Accepted
time: 0ms
memory: 3712kb

input:

10 3

output:

299

result:

ok 1 number(s): "299"

Test #9:

score: 0
Accepted
time: 0ms
memory: 3648kb

input:

10 4

output:

743

result:

ok 1 number(s): "743"

Test #10:

score: 0
Accepted
time: 0ms
memory: 3712kb

input:

10 5

output:

1129

result:

ok 1 number(s): "1129"

Test #11:

score: 0
Accepted
time: 0ms
memory: 3800kb

input:

15 6

output:

28006

result:

ok 1 number(s): "28006"

Test #12:

score: 0
Accepted
time: 0ms
memory: 3716kb

input:

15 7

output:

42035

result:

ok 1 number(s): "42035"

Test #13:

score: 0
Accepted
time: 0ms
memory: 3736kb

input:

123 45

output:

214851327

result:

ok 1 number(s): "214851327"

Test #14:

score: 0
Accepted
time: 1ms
memory: 4088kb

input:

998 244

output:

964050559

result:

ok 1 number(s): "964050559"

Test #15:

score: 0
Accepted
time: 3ms
memory: 4328kb

input:

1919 810

output:

379720338

result:

ok 1 number(s): "379720338"

Test #16:

score: 0
Accepted
time: 2ms
memory: 3888kb

input:

1048 576

output:

216543264

result:

ok 1 number(s): "216543264"

Test #17:

score: 0
Accepted
time: 1ms
memory: 3868kb

input:

999 777

output:

635548531

result:

ok 1 number(s): "635548531"

Test #18:

score: 0
Accepted
time: 330ms
memory: 35668kb

input:

99999 77777

output:

448144614

result:

ok 1 number(s): "448144614"

Test #19:

score: 0
Accepted
time: 96ms
memory: 13904kb

input:

34527 6545

output:

748108997

result:

ok 1 number(s): "748108997"

Test #20:

score: 0
Accepted
time: 26ms
memory: 6596kb

input:

12345 12

output:

777496209

result:

ok 1 number(s): "777496209"

Test #21:

score: 0
Accepted
time: 0ms
memory: 3656kb

input:

1 1

output:

0

result:

ok 1 number(s): "0"

Test #22:

score: 0
Accepted
time: 318ms
memory: 35592kb

input:

100000 10101

output:

855985819

result:

ok 1 number(s): "855985819"

Test #23:

score: 0
Accepted
time: 327ms
memory: 35580kb

input:

100000 91919

output:

92446940

result:

ok 1 number(s): "92446940"

Test #24:

score: 0
Accepted
time: 331ms
memory: 35592kb

input:

100000 77979

output:

106899398

result:

ok 1 number(s): "106899398"

Test #25:

score: 0
Accepted
time: 17ms
memory: 6100kb

input:

10000 11

output:

326411649

result:

ok 1 number(s): "326411649"

Test #26:

score: 0
Accepted
time: 314ms
memory: 35576kb

input:

100000 2

output:

15322970

result:

ok 1 number(s): "15322970"

Test #27:

score: 0
Accepted
time: 314ms
memory: 35672kb

input:

100000 3

output:

93355797

result:

ok 1 number(s): "93355797"

Test #28:

score: 0
Accepted
time: 317ms
memory: 35704kb

input:

100000 99998

output:

331850772

result:

ok 1 number(s): "331850772"

Test #29:

score: 0
Accepted
time: 316ms
memory: 35540kb

input:

100000 99996

output:

885066226

result:

ok 1 number(s): "885066226"

Test #30:

score: 0
Accepted
time: 24ms
memory: 6944kb

input:

13115 2964

output:

0

result:

ok 1 number(s): "0"

Test #31:

score: 0
Accepted
time: 327ms
memory: 35660kb

input:

100000 17

output:

425792977

result:

ok 1 number(s): "425792977"

Test #32:

score: 0
Accepted
time: 332ms
memory: 35576kb

input:

99991 16

output:

667323936

result:

ok 1 number(s): "667323936"

Test #33:

score: 0
Accepted
time: 329ms
memory: 35748kb

input:

99991 17

output:

627396741

result:

ok 1 number(s): "627396741"

Test #34:

score: 0
Accepted
time: 328ms
memory: 35704kb

input:

99991 18

output:

874158501

result:

ok 1 number(s): "874158501"

Test #35:

score: 0
Accepted
time: 324ms
memory: 35740kb

input:

100000 100000

output:

99999

result:

ok 1 number(s): "99999"

Test #36:

score: 0
Accepted
time: 309ms
memory: 33704kb

input:

94229 94229

output:

94228

result:

ok 1 number(s): "94228"

Test #37:

score: 0
Accepted
time: 301ms
memory: 33472kb

input:

94229 94223

output:

476599876

result:

ok 1 number(s): "476599876"

Test #38:

score: 0
Accepted
time: 0ms
memory: 3668kb

input:

2 1

output:

0

result:

ok 1 number(s): "0"

Test #39:

score: 0
Accepted
time: 0ms
memory: 3776kb

input:

2 2

output:

0

result:

ok 1 number(s): "0"

Test #40:

score: 0
Accepted
time: 0ms
memory: 3680kb

input:

3 1

output:

0

result:

ok 1 number(s): "0"

Test #41:

score: 0
Accepted
time: 0ms
memory: 3680kb

input:

3 2

output:

2

result:

ok 1 number(s): "2"

Test #42:

score: 0
Accepted
time: 0ms
memory: 3652kb

input:

3 3

output:

2

result:

ok 1 number(s): "2"

Test #43:

score: 0
Accepted
time: 0ms
memory: 3860kb

input:

9 2

output:

44

result:

ok 1 number(s): "44"

Test #44:

score: 0
Accepted
time: 0ms
memory: 3792kb

input:

9 3

output:

206

result:

ok 1 number(s): "206"

Test #45:

score: 0
Accepted
time: 0ms
memory: 3620kb

input:

9 4

output:

441

result:

ok 1 number(s): "441"

Test #46:

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

input:

9 7

output:

224

result:

ok 1 number(s): "224"

Test #47:

score: 0
Accepted
time: 199ms
memory: 25552kb

input:

70839 22229

output:

0

result:

ok 1 number(s): "0"

Test #48:

score: 0
Accepted
time: 198ms
memory: 23700kb

input:

65536 17

output:

698801006

result:

ok 1 number(s): "698801006"

Test #49:

score: 0
Accepted
time: 190ms
memory: 23704kb

input:

65535 17

output:

433312902

result:

ok 1 number(s): "433312902"

Test #50:

score: 0
Accepted
time: 343ms
memory: 35772kb

input:

99856 317

output:

932131332

result:

ok 1 number(s): "932131332"

Test #51:

score: 0
Accepted
time: 334ms
memory: 35588kb

input:

99856 318

output:

398997854

result:

ok 1 number(s): "398997854"

Test #52:

score: 0
Accepted
time: 354ms
memory: 35668kb

input:

99856 2

output:

984791559

result:

ok 1 number(s): "984791559"

Test #53:

score: 0
Accepted
time: 323ms
memory: 35672kb

input:

100000 50000

output:

309108799

result:

ok 1 number(s): "309108799"

Extra Test:

score: 0
Extra Test Passed