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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#772314 | #9553. The Hermit | Martian148 | AC ✓ | 111ms | 31756kb | C++20 | 1.5kb | 2024-11-22 18:37:51 | 2024-11-22 18:37:52 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
constexpr ll TT = 998244353;
ll qpow(ll a, ll b) {
ll res = 1;
while (b) {
if (b & 1) res = res * a % TT;
a = a * a % TT;
b >>= 1;
}
return res;
}
int main() {
int n, m; cin >> m >> n;
vector<ll> Fac(m + 1, 1), Inv(m + 1, 1);
for (int i = 1; i <= m; i++) Fac[i] = Fac[i - 1] * i % TT;
Inv[m] = qpow(Fac[m], TT - 2);
for (int i = m - 1; i >= 0; i--) Inv[i] = Inv[i + 1] * (i + 1) % TT;
auto C = [&] (int a, int b) -> ll {
if (a < b) return 0ll;
return Fac[a] * Inv[b] % TT * Inv[a - b] % TT;
};
ll ans = 0, all = C(m, n) * n % TT;
vector dp(21, vector<ll>(m + 1, 0)); // dp[c][x] 表示长度为 c 的序列,最后一个是 x 的方案数
vector<vector<int>> prime(m + 1);
for (int i = 1; i <= m; i++)
for (int j = i * 2; j <= m; j += i)
prime[j].push_back(i);
for (int i = 1; i <= m; i++) dp[1][i] = 1;
for (int c = 2; c <= 20; c++) {
for (int x = 1; x <= m; x++) {
for (auto y : prime[x]) {
dp[c][x] = (dp[c][x] + dp[c - 1][y]) % TT;
}
}
}
for (int i = 1; i <= m; i++) {
for (int j = 1; j <= min(n, 20); j++) {
ll now = dp[j][i] * C(m / i - 1, n - j) % TT;
ans = (ans + now) % TT;
}
}
cout << ((all - ans) % TT + TT) % TT << endl;
return 0;
}
这程序好像有点Bug,我给组数据试试?
Details
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Test #1:
score: 100
Accepted
time: 0ms
memory: 3636kb
input:
4 3
output:
7
result:
ok 1 number(s): "7"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3576kb
input:
11 4
output:
1187
result:
ok 1 number(s): "1187"
Test #3:
score: 0
Accepted
time: 111ms
memory: 31572kb
input:
100000 99999
output:
17356471
result:
ok 1 number(s): "17356471"
Test #4:
score: 0
Accepted
time: 6ms
memory: 6420kb
input:
11451 1919
output:
845616153
result:
ok 1 number(s): "845616153"
Test #5:
score: 0
Accepted
time: 107ms
memory: 31736kb
input:
99998 12345
output:
936396560
result:
ok 1 number(s): "936396560"
Test #6:
score: 0
Accepted
time: 98ms
memory: 31556kb
input:
100000 1
output:
0
result:
ok 1 number(s): "0"
Test #7:
score: 0
Accepted
time: 101ms
memory: 31664kb
input:
100000 15
output:
190067060
result:
ok 1 number(s): "190067060"
Test #8:
score: 0
Accepted
time: 0ms
memory: 3600kb
input:
10 3
output:
299
result:
ok 1 number(s): "299"
Test #9:
score: 0
Accepted
time: 0ms
memory: 3488kb
input:
10 4
output:
743
result:
ok 1 number(s): "743"
Test #10:
score: 0
Accepted
time: 0ms
memory: 3764kb
input:
10 5
output:
1129
result:
ok 1 number(s): "1129"
Test #11:
score: 0
Accepted
time: 0ms
memory: 3796kb
input:
15 6
output:
28006
result:
ok 1 number(s): "28006"
Test #12:
score: 0
Accepted
time: 0ms
memory: 3604kb
input:
15 7
output:
42035
result:
ok 1 number(s): "42035"
Test #13:
score: 0
Accepted
time: 0ms
memory: 3572kb
input:
123 45
output:
214851327
result:
ok 1 number(s): "214851327"
Test #14:
score: 0
Accepted
time: 1ms
memory: 3868kb
input:
998 244
output:
964050559
result:
ok 1 number(s): "964050559"
Test #15:
score: 0
Accepted
time: 1ms
memory: 4160kb
input:
1919 810
output:
379720338
result:
ok 1 number(s): "379720338"
Test #16:
score: 0
Accepted
time: 1ms
memory: 3840kb
input:
1048 576
output:
216543264
result:
ok 1 number(s): "216543264"
Test #17:
score: 0
Accepted
time: 1ms
memory: 3836kb
input:
999 777
output:
635548531
result:
ok 1 number(s): "635548531"
Test #18:
score: 0
Accepted
time: 103ms
memory: 31644kb
input:
99999 77777
output:
448144614
result:
ok 1 number(s): "448144614"
Test #19:
score: 0
Accepted
time: 30ms
memory: 12964kb
input:
34527 6545
output:
748108997
result:
ok 1 number(s): "748108997"
Test #20:
score: 0
Accepted
time: 9ms
memory: 6696kb
input:
12345 12
output:
777496209
result:
ok 1 number(s): "777496209"
Test #21:
score: 0
Accepted
time: 0ms
memory: 3536kb
input:
1 1
output:
0
result:
ok 1 number(s): "0"
Test #22:
score: 0
Accepted
time: 94ms
memory: 31756kb
input:
100000 10101
output:
855985819
result:
ok 1 number(s): "855985819"
Test #23:
score: 0
Accepted
time: 108ms
memory: 31644kb
input:
100000 91919
output:
92446940
result:
ok 1 number(s): "92446940"
Test #24:
score: 0
Accepted
time: 96ms
memory: 31568kb
input:
100000 77979
output:
106899398
result:
ok 1 number(s): "106899398"
Test #25:
score: 0
Accepted
time: 7ms
memory: 6344kb
input:
10000 11
output:
326411649
result:
ok 1 number(s): "326411649"
Test #26:
score: 0
Accepted
time: 102ms
memory: 31696kb
input:
100000 2
output:
15322970
result:
ok 1 number(s): "15322970"
Test #27:
score: 0
Accepted
time: 98ms
memory: 31496kb
input:
100000 3
output:
93355797
result:
ok 1 number(s): "93355797"
Test #28:
score: 0
Accepted
time: 102ms
memory: 31520kb
input:
100000 99998
output:
331850772
result:
ok 1 number(s): "331850772"
Test #29:
score: 0
Accepted
time: 103ms
memory: 31648kb
input:
100000 99996
output:
885066226
result:
ok 1 number(s): "885066226"
Test #30:
score: 0
Accepted
time: 11ms
memory: 6868kb
input:
13115 2964
output:
0
result:
ok 1 number(s): "0"
Test #31:
score: 0
Accepted
time: 105ms
memory: 31692kb
input:
100000 17
output:
425792977
result:
ok 1 number(s): "425792977"
Test #32:
score: 0
Accepted
time: 108ms
memory: 31740kb
input:
99991 16
output:
667323936
result:
ok 1 number(s): "667323936"
Test #33:
score: 0
Accepted
time: 99ms
memory: 31588kb
input:
99991 17
output:
627396741
result:
ok 1 number(s): "627396741"
Test #34:
score: 0
Accepted
time: 105ms
memory: 31580kb
input:
99991 18
output:
874158501
result:
ok 1 number(s): "874158501"
Test #35:
score: 0
Accepted
time: 103ms
memory: 31584kb
input:
100000 100000
output:
99999
result:
ok 1 number(s): "99999"
Test #36:
score: 0
Accepted
time: 104ms
memory: 29844kb
input:
94229 94229
output:
94228
result:
ok 1 number(s): "94228"
Test #37:
score: 0
Accepted
time: 94ms
memory: 29808kb
input:
94229 94223
output:
476599876
result:
ok 1 number(s): "476599876"
Test #38:
score: 0
Accepted
time: 0ms
memory: 3600kb
input:
2 1
output:
0
result:
ok 1 number(s): "0"
Test #39:
score: 0
Accepted
time: 0ms
memory: 3832kb
input:
2 2
output:
0
result:
ok 1 number(s): "0"
Test #40:
score: 0
Accepted
time: 0ms
memory: 3836kb
input:
3 1
output:
0
result:
ok 1 number(s): "0"
Test #41:
score: 0
Accepted
time: 0ms
memory: 3604kb
input:
3 2
output:
2
result:
ok 1 number(s): "2"
Test #42:
score: 0
Accepted
time: 0ms
memory: 3536kb
input:
3 3
output:
2
result:
ok 1 number(s): "2"
Test #43:
score: 0
Accepted
time: 0ms
memory: 3528kb
input:
9 2
output:
44
result:
ok 1 number(s): "44"
Test #44:
score: 0
Accepted
time: 0ms
memory: 3564kb
input:
9 3
output:
206
result:
ok 1 number(s): "206"
Test #45:
score: 0
Accepted
time: 0ms
memory: 3520kb
input:
9 4
output:
441
result:
ok 1 number(s): "441"
Test #46:
score: 0
Accepted
time: 0ms
memory: 3596kb
input:
9 7
output:
224
result:
ok 1 number(s): "224"
Test #47:
score: 0
Accepted
time: 72ms
memory: 23340kb
input:
70839 22229
output:
0
result:
ok 1 number(s): "0"
Test #48:
score: 0
Accepted
time: 61ms
memory: 21664kb
input:
65536 17
output:
698801006
result:
ok 1 number(s): "698801006"
Test #49:
score: 0
Accepted
time: 62ms
memory: 21744kb
input:
65535 17
output:
433312902
result:
ok 1 number(s): "433312902"
Test #50:
score: 0
Accepted
time: 105ms
memory: 31752kb
input:
99856 317
output:
932131332
result:
ok 1 number(s): "932131332"
Test #51:
score: 0
Accepted
time: 111ms
memory: 31524kb
input:
99856 318
output:
398997854
result:
ok 1 number(s): "398997854"
Test #52:
score: 0
Accepted
time: 102ms
memory: 31744kb
input:
99856 2
output:
984791559
result:
ok 1 number(s): "984791559"
Test #53:
score: 0
Accepted
time: 102ms
memory: 31584kb
input:
100000 50000
output:
309108799
result:
ok 1 number(s): "309108799"
Extra Test:
score: 0
Extra Test Passed