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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#775484 | #9553. The Hermit | guiyuan98# | AC ✓ | 186ms | 33496kb | C++20 | 1.9kb | 2024-11-23 16:03:24 | 2024-11-23 16:03:25 |
Judging History
answer
#include <bits/stdc++.h>
using i64 = long long;
const int N = 1e5 + 10;
const int MOD = 998244353;
std::vector<i64> fac(N + 1, 1), invfac(N + 1, 1);
i64 ksm(i64 a, i64 n, i64 MOD) {
i64 ans = 1;
a = (a % MOD + MOD) % MOD;
while (n) {
if (n & 1) {
ans = (a * ans) % MOD;
}
a = (a * a) % MOD;
n >>= 1;
}
return ans;
}
void init(int n) {
fac[0] = 1;
for (int i = 1; i <= n; i++) {
fac[i] = fac[i - 1] * i % MOD;
}
invfac[n] = ksm(fac[n], MOD - 2, MOD);
for (int i = n - 1; i >= 0; i--) {
invfac[i] = invfac[i + 1] * (i + 1) % MOD;
}
}
i64 C(int n, int m) { // 组合数
if (m > n || m < 0) {
return 0;
}
return fac[n] * invfac[m] % MOD * invfac[n - m] % MOD;
}
i64 A(int n, int m) { // 排列数
if (m > n || m < 0) {
return 0;
}
return fac[n] * invfac[n - m] % MOD;
}
i64 catalan(int n) { // 卡特兰数
if (n < 0) {
return 0;
}
return C(2 * n, n) * ksm(n + 1, MOD - 2, MOD) % MOD;
}
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(0);
std::cout.tie(0);
init(N);
int m, n;
std::cin >> m >> n;
std::unordered_map<int, std::unordered_map<int, int>> f;
for (int x = 1; x <= m; x++) {
f[1][x] = 1;
}
int ans = n * C(m, n) % MOD;
for (int i = 1; i <= n; i++) { // 枚举长度
for (auto [x, y] : f[i]) {
ans = ans - f[i][x] * C(m / x - 1, n - i) % MOD; // 直接枚举倍数
ans %= MOD;
if (ans < 0) {
ans += MOD;
}
for (int j = 2; j * x <= m && i + 1 <= n; j++) { // 更新倍数链
f[i + 1][j * x] = (f[i + 1][j * x] + f[i][x]) % MOD;
}
}
}
std::cout << ans << '\n';
}
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Details
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Test #1:
score: 100
Accepted
time: 2ms
memory: 4640kb
input:
4 3
output:
7
result:
ok 1 number(s): "7"
Test #2:
score: 0
Accepted
time: 2ms
memory: 4588kb
input:
11 4
output:
1187
result:
ok 1 number(s): "1187"
Test #3:
score: 0
Accepted
time: 186ms
memory: 33496kb
input:
100000 99999
output:
17356471
result:
ok 1 number(s): "17356471"
Test #4:
score: 0
Accepted
time: 14ms
memory: 7000kb
input:
11451 1919
output:
845616153
result:
ok 1 number(s): "845616153"
Test #5:
score: 0
Accepted
time: 173ms
memory: 25468kb
input:
99998 12345
output:
936396560
result:
ok 1 number(s): "936396560"
Test #6:
score: 0
Accepted
time: 9ms
memory: 9440kb
input:
100000 1
output:
0
result:
ok 1 number(s): "0"
Test #7:
score: 0
Accepted
time: 168ms
memory: 24196kb
input:
100000 15
output:
190067060
result:
ok 1 number(s): "190067060"
Test #8:
score: 0
Accepted
time: 2ms
memory: 4540kb
input:
10 3
output:
299
result:
ok 1 number(s): "299"
Test #9:
score: 0
Accepted
time: 2ms
memory: 4544kb
input:
10 4
output:
743
result:
ok 1 number(s): "743"
Test #10:
score: 0
Accepted
time: 2ms
memory: 4512kb
input:
10 5
output:
1129
result:
ok 1 number(s): "1129"
Test #11:
score: 0
Accepted
time: 2ms
memory: 4728kb
input:
15 6
output:
28006
result:
ok 1 number(s): "28006"
Test #12:
score: 0
Accepted
time: 2ms
memory: 4732kb
input:
15 7
output:
42035
result:
ok 1 number(s): "42035"
Test #13:
score: 0
Accepted
time: 2ms
memory: 4540kb
input:
123 45
output:
214851327
result:
ok 1 number(s): "214851327"
Test #14:
score: 0
Accepted
time: 2ms
memory: 4972kb
input:
998 244
output:
964050559
result:
ok 1 number(s): "964050559"
Test #15:
score: 0
Accepted
time: 0ms
memory: 5160kb
input:
1919 810
output:
379720338
result:
ok 1 number(s): "379720338"
Test #16:
score: 0
Accepted
time: 0ms
memory: 5048kb
input:
1048 576
output:
216543264
result:
ok 1 number(s): "216543264"
Test #17:
score: 0
Accepted
time: 2ms
memory: 5020kb
input:
999 777
output:
635548531
result:
ok 1 number(s): "635548531"
Test #18:
score: 0
Accepted
time: 179ms
memory: 31016kb
input:
99999 77777
output:
448144614
result:
ok 1 number(s): "448144614"
Test #19:
score: 0
Accepted
time: 42ms
memory: 11564kb
input:
34527 6545
output:
748108997
result:
ok 1 number(s): "748108997"
Test #20:
score: 0
Accepted
time: 14ms
memory: 7164kb
input:
12345 12
output:
777496209
result:
ok 1 number(s): "777496209"
Test #21:
score: 0
Accepted
time: 2ms
memory: 4584kb
input:
1 1
output:
0
result:
ok 1 number(s): "0"
Test #22:
score: 0
Accepted
time: 176ms
memory: 25168kb
input:
100000 10101
output:
855985819
result:
ok 1 number(s): "855985819"
Test #23:
score: 0
Accepted
time: 173ms
memory: 32888kb
input:
100000 91919
output:
92446940
result:
ok 1 number(s): "92446940"
Test #24:
score: 0
Accepted
time: 177ms
memory: 31060kb
input:
100000 77979
output:
106899398
result:
ok 1 number(s): "106899398"
Test #25:
score: 0
Accepted
time: 11ms
memory: 6604kb
input:
10000 11
output:
326411649
result:
ok 1 number(s): "326411649"
Test #26:
score: 0
Accepted
time: 51ms
memory: 13900kb
input:
100000 2
output:
15322970
result:
ok 1 number(s): "15322970"
Test #27:
score: 0
Accepted
time: 101ms
memory: 18304kb
input:
100000 3
output:
93355797
result:
ok 1 number(s): "93355797"
Test #28:
score: 0
Accepted
time: 180ms
memory: 33440kb
input:
100000 99998
output:
331850772
result:
ok 1 number(s): "331850772"
Test #29:
score: 0
Accepted
time: 169ms
memory: 33356kb
input:
100000 99996
output:
885066226
result:
ok 1 number(s): "885066226"
Test #30:
score: 0
Accepted
time: 12ms
memory: 7528kb
input:
13115 2964
output:
0
result:
ok 1 number(s): "0"
Test #31:
score: 0
Accepted
time: 162ms
memory: 24128kb
input:
100000 17
output:
425792977
result:
ok 1 number(s): "425792977"
Test #32:
score: 0
Accepted
time: 166ms
memory: 24176kb
input:
99991 16
output:
667323936
result:
ok 1 number(s): "667323936"
Test #33:
score: 0
Accepted
time: 179ms
memory: 24124kb
input:
99991 17
output:
627396741
result:
ok 1 number(s): "627396741"
Test #34:
score: 0
Accepted
time: 176ms
memory: 24116kb
input:
99991 18
output:
874158501
result:
ok 1 number(s): "874158501"
Test #35:
score: 0
Accepted
time: 173ms
memory: 33340kb
input:
100000 100000
output:
99999
result:
ok 1 number(s): "99999"
Test #36:
score: 0
Accepted
time: 162ms
memory: 31588kb
input:
94229 94229
output:
94228
result:
ok 1 number(s): "94228"
Test #37:
score: 0
Accepted
time: 173ms
memory: 31508kb
input:
94229 94223
output:
476599876
result:
ok 1 number(s): "476599876"
Test #38:
score: 0
Accepted
time: 2ms
memory: 4416kb
input:
2 1
output:
0
result:
ok 1 number(s): "0"
Test #39:
score: 0
Accepted
time: 0ms
memory: 4592kb
input:
2 2
output:
0
result:
ok 1 number(s): "0"
Test #40:
score: 0
Accepted
time: 2ms
memory: 4640kb
input:
3 1
output:
0
result:
ok 1 number(s): "0"
Test #41:
score: 0
Accepted
time: 2ms
memory: 4588kb
input:
3 2
output:
2
result:
ok 1 number(s): "2"
Test #42:
score: 0
Accepted
time: 0ms
memory: 4584kb
input:
3 3
output:
2
result:
ok 1 number(s): "2"
Test #43:
score: 0
Accepted
time: 2ms
memory: 4540kb
input:
9 2
output:
44
result:
ok 1 number(s): "44"
Test #44:
score: 0
Accepted
time: 2ms
memory: 4728kb
input:
9 3
output:
206
result:
ok 1 number(s): "206"
Test #45:
score: 0
Accepted
time: 2ms
memory: 4556kb
input:
9 4
output:
441
result:
ok 1 number(s): "441"
Test #46:
score: 0
Accepted
time: 2ms
memory: 4444kb
input:
9 7
output:
224
result:
ok 1 number(s): "224"
Test #47:
score: 0
Accepted
time: 102ms
memory: 20060kb
input:
70839 22229
output:
0
result:
ok 1 number(s): "0"
Test #48:
score: 0
Accepted
time: 82ms
memory: 17064kb
input:
65536 17
output:
698801006
result:
ok 1 number(s): "698801006"
Test #49:
score: 0
Accepted
time: 84ms
memory: 17232kb
input:
65535 17
output:
433312902
result:
ok 1 number(s): "433312902"
Test #50:
score: 0
Accepted
time: 168ms
memory: 24108kb
input:
99856 317
output:
932131332
result:
ok 1 number(s): "932131332"
Test #51:
score: 0
Accepted
time: 172ms
memory: 24160kb
input:
99856 318
output:
398997854
result:
ok 1 number(s): "398997854"
Test #52:
score: 0
Accepted
time: 56ms
memory: 13960kb
input:
99856 2
output:
984791559
result:
ok 1 number(s): "984791559"
Test #53:
score: 0
Accepted
time: 170ms
memory: 28952kb
input:
100000 50000
output:
309108799
result:
ok 1 number(s): "309108799"
Extra Test:
score: 0
Extra Test Passed