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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#755503 | #9553. The Hermit | ucup-team1264# | AC ✓ | 148ms | 33008kb | C++20 | 2.2kb | 2024-11-16 17:31:23 | 2024-11-16 17:31:23 |
Judging History
你现在查看的是测评时间为 2024-11-16 17:31:23 的历史记录
- [2024-11-18 19:43:48]
- hack成功,自动添加数据
- (/hack/1196)
- [2024-11-16 17:31:23]
- 提交
answer
#include <bits/stdc++.h>
using namespace std;
using i64 = int64_t;
constexpr i64 MOD = 998244353, N = 1e5 + 1145;
i64 fact[N + 1], inv_fact[N + 1], mu[N + 1], is_prime[N + 1];
vector<int> prs;
i64 inv(i64 x) {
i64 res = 1, pw = MOD - 2;
while (pw) {
if (pw & 1) (res *= x) %= MOD;
(x *= x) %= MOD;
pw >>= 1;
}
return res;
}
i64 dp[20][N + 1];
vector<int> fac[N + 1];
i64 comb(int n, int m) {
if (m < 0 || n < m) return 0;
return fact[n] * inv_fact[m] % MOD * inv_fact[n - m] % MOD;
}
void get_mu(int n) {
fill(is_prime + 1, is_prime + n + 1, 1);
mu[1] = 1;
for (int i = 2; i <= n; i++) {
if (is_prime[i]) mu[i] = -1, prs.push_back(i);
for (int p : prs) {
if (p > n / i) break;
is_prime[i * p] = false;
mu[i * p] = mu[i] * (i % p ? -1 : 0);
if (i % p == 0) break;
}
}
}
int main() {
int n, m; cin >> m >> n;
get_mu(m);
fact[0] = 1;
for (int i = 1; i <= m; i++) fact[i] = fact[i - 1] * i % MOD;
inv_fact[m] = inv(fact[m]);
for (int i = m - 1; i >= 0; i--) inv_fact[i] = inv_fact[i + 1] * (i + 1) % MOD;
for (int i = 1; i <= m; i++) {
for (int j = i + i; j <= m; j += i) {
fac[j].push_back(i);
}
}
auto get = [&](int n, int c) {
i64 res = comb(n - 1, c);
for (int i = 2; i <= n; i++) {
res += mu[i] * comb(n / i, c);
}
return res % MOD;
};
i64 ans = 0;
for (int i = 1; i <= m; i++) {
dp[0][i] = dp[1][i] = 1;
for (int c = 2; c < 20; c++) {
for (int j: fac[i]) (dp[c][i] += dp[c - 1][j]) %= MOD;
}
i64 t[20];
for (int c = 0; c < 20; c++) {
t[c] = dp[c][i];
if (c > 0) for (int j: fac[i]) t[c] += dp[c][j];
t[c] %= MOD;
}
for (int c = 0; c < 20; c++) {
ans += (t[c] * get(m / i, n - c)) % MOD * (n - c) % MOD;
// if (i == 1) {
// cout << format("{} {} {}\n", c, dp[c][i], get(m / i, n - c));
// }
}
ans %= MOD;
}
(ans += MOD) %= MOD;
cout << ans << "\n";
}
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: 1ms
memory: 7828kb
input:
4 3
output:
7
result:
ok 1 number(s): "7"
Test #2:
score: 0
Accepted
time: 0ms
memory: 9772kb
input:
11 4
output:
1187
result:
ok 1 number(s): "1187"
Test #3:
score: 0
Accepted
time: 125ms
memory: 32844kb
input:
100000 99999
output:
17356471
result:
ok 1 number(s): "17356471"
Test #4:
score: 0
Accepted
time: 14ms
memory: 14500kb
input:
11451 1919
output:
845616153
result:
ok 1 number(s): "845616153"
Test #5:
score: 0
Accepted
time: 139ms
memory: 32912kb
input:
99998 12345
output:
936396560
result:
ok 1 number(s): "936396560"
Test #6:
score: 0
Accepted
time: 146ms
memory: 32876kb
input:
100000 1
output:
0
result:
ok 1 number(s): "0"
Test #7:
score: 0
Accepted
time: 137ms
memory: 33008kb
input:
100000 15
output:
190067060
result:
ok 1 number(s): "190067060"
Test #8:
score: 0
Accepted
time: 2ms
memory: 11968kb
input:
10 3
output:
299
result:
ok 1 number(s): "299"
Test #9:
score: 0
Accepted
time: 0ms
memory: 9864kb
input:
10 4
output:
743
result:
ok 1 number(s): "743"
Test #10:
score: 0
Accepted
time: 0ms
memory: 9780kb
input:
10 5
output:
1129
result:
ok 1 number(s): "1129"
Test #11:
score: 0
Accepted
time: 2ms
memory: 11820kb
input:
15 6
output:
28006
result:
ok 1 number(s): "28006"
Test #12:
score: 0
Accepted
time: 1ms
memory: 9840kb
input:
15 7
output:
42035
result:
ok 1 number(s): "42035"
Test #13:
score: 0
Accepted
time: 1ms
memory: 7808kb
input:
123 45
output:
214851327
result:
ok 1 number(s): "214851327"
Test #14:
score: 0
Accepted
time: 2ms
memory: 12100kb
input:
998 244
output:
964050559
result:
ok 1 number(s): "964050559"
Test #15:
score: 0
Accepted
time: 0ms
memory: 10292kb
input:
1919 810
output:
379720338
result:
ok 1 number(s): "379720338"
Test #16:
score: 0
Accepted
time: 0ms
memory: 8060kb
input:
1048 576
output:
216543264
result:
ok 1 number(s): "216543264"
Test #17:
score: 0
Accepted
time: 0ms
memory: 7980kb
input:
999 777
output:
635548531
result:
ok 1 number(s): "635548531"
Test #18:
score: 0
Accepted
time: 148ms
memory: 32972kb
input:
99999 77777
output:
448144614
result:
ok 1 number(s): "448144614"
Test #19:
score: 0
Accepted
time: 40ms
memory: 17744kb
input:
34527 6545
output:
748108997
result:
ok 1 number(s): "748108997"
Test #20:
score: 0
Accepted
time: 12ms
memory: 14628kb
input:
12345 12
output:
777496209
result:
ok 1 number(s): "777496209"
Test #21:
score: 0
Accepted
time: 1ms
memory: 7664kb
input:
1 1
output:
0
result:
ok 1 number(s): "0"
Test #22:
score: 0
Accepted
time: 145ms
memory: 32864kb
input:
100000 10101
output:
855985819
result:
ok 1 number(s): "855985819"
Test #23:
score: 0
Accepted
time: 132ms
memory: 32980kb
input:
100000 91919
output:
92446940
result:
ok 1 number(s): "92446940"
Test #24:
score: 0
Accepted
time: 141ms
memory: 32876kb
input:
100000 77979
output:
106899398
result:
ok 1 number(s): "106899398"
Test #25:
score: 0
Accepted
time: 8ms
memory: 10272kb
input:
10000 11
output:
326411649
result:
ok 1 number(s): "326411649"
Test #26:
score: 0
Accepted
time: 143ms
memory: 32916kb
input:
100000 2
output:
15322970
result:
ok 1 number(s): "15322970"
Test #27:
score: 0
Accepted
time: 139ms
memory: 32992kb
input:
100000 3
output:
93355797
result:
ok 1 number(s): "93355797"
Test #28:
score: 0
Accepted
time: 127ms
memory: 32872kb
input:
100000 99998
output:
331850772
result:
ok 1 number(s): "331850772"
Test #29:
score: 0
Accepted
time: 141ms
memory: 32876kb
input:
100000 99996
output:
885066226
result:
ok 1 number(s): "885066226"
Test #30:
score: 0
Accepted
time: 16ms
memory: 14756kb
input:
13115 2964
output:
0
result:
ok 1 number(s): "0"
Test #31:
score: 0
Accepted
time: 140ms
memory: 32872kb
input:
100000 17
output:
425792977
result:
ok 1 number(s): "425792977"
Test #32:
score: 0
Accepted
time: 140ms
memory: 32940kb
input:
99991 16
output:
667323936
result:
ok 1 number(s): "667323936"
Test #33:
score: 0
Accepted
time: 145ms
memory: 32912kb
input:
99991 17
output:
627396741
result:
ok 1 number(s): "627396741"
Test #34:
score: 0
Accepted
time: 139ms
memory: 32928kb
input:
99991 18
output:
874158501
result:
ok 1 number(s): "874158501"
Test #35:
score: 0
Accepted
time: 131ms
memory: 32924kb
input:
100000 100000
output:
99999
result:
ok 1 number(s): "99999"
Test #36:
score: 0
Accepted
time: 112ms
memory: 31344kb
input:
94229 94229
output:
94228
result:
ok 1 number(s): "94228"
Test #37:
score: 0
Accepted
time: 117ms
memory: 31444kb
input:
94229 94223
output:
476599876
result:
ok 1 number(s): "476599876"
Test #38:
score: 0
Accepted
time: 1ms
memory: 7868kb
input:
2 1
output:
0
result:
ok 1 number(s): "0"
Test #39:
score: 0
Accepted
time: 0ms
memory: 11884kb
input:
2 2
output:
0
result:
ok 1 number(s): "0"
Test #40:
score: 0
Accepted
time: 1ms
memory: 9840kb
input:
3 1
output:
0
result:
ok 1 number(s): "0"
Test #41:
score: 0
Accepted
time: 0ms
memory: 9904kb
input:
3 2
output:
2
result:
ok 1 number(s): "2"
Test #42:
score: 0
Accepted
time: 2ms
memory: 9824kb
input:
3 3
output:
2
result:
ok 1 number(s): "2"
Test #43:
score: 0
Accepted
time: 1ms
memory: 9776kb
input:
9 2
output:
44
result:
ok 1 number(s): "44"
Test #44:
score: 0
Accepted
time: 0ms
memory: 9840kb
input:
9 3
output:
206
result:
ok 1 number(s): "206"
Test #45:
score: 0
Accepted
time: 0ms
memory: 9768kb
input:
9 4
output:
441
result:
ok 1 number(s): "441"
Test #46:
score: 0
Accepted
time: 1ms
memory: 9852kb
input:
9 7
output:
224
result:
ok 1 number(s): "224"
Test #47:
score: 0
Accepted
time: 88ms
memory: 26212kb
input:
70839 22229
output:
0
result:
ok 1 number(s): "0"
Test #48:
score: 0
Accepted
time: 93ms
memory: 25060kb
input:
65536 17
output:
698801006
result:
ok 1 number(s): "698801006"
Test #49:
score: 0
Accepted
time: 83ms
memory: 24464kb
input:
65535 17
output:
433312902
result:
ok 1 number(s): "433312902"
Test #50:
score: 0
Accepted
time: 127ms
memory: 32808kb
input:
99856 317
output:
932131332
result:
ok 1 number(s): "932131332"
Test #51:
score: 0
Accepted
time: 120ms
memory: 32860kb
input:
99856 318
output:
398997854
result:
ok 1 number(s): "398997854"
Test #52:
score: 0
Accepted
time: 131ms
memory: 32972kb
input:
99856 2
output:
984791559
result:
ok 1 number(s): "984791559"
Test #53:
score: 0
Accepted
time: 135ms
memory: 32928kb
input:
100000 50000
output:
309108799
result:
ok 1 number(s): "309108799"
Extra Test:
score: 0
Extra Test Passed