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ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#174390 | #6417. Classical Summation Problem | alexzhanUS | AC ✓ | 467ms | 3608kb | C++17 | 2.1kb | 2023-09-10 07:01:51 | 2023-09-10 07:01:52 |
Judging History
answer
#include <iostream>
#include <vector>
using namespace std;
long long modulo = 998244353;
long long binaryExponentiation(long long value, long long power) {
vector<long long> powers(31);
powers[0] = value;
for (int i = 1; i <= 30; i++) {
powers[i] = powers[i - 1] * powers[i - 1];
powers[i] %= modulo;
}
long long answer = 1;
for (int i = 0; i <= 30; i++) {
if ((power & (1 << i)) > 0) {
answer *= powers[i];
answer %= modulo;
}
}
return answer;
}
long long divide(long long a, long long b) {
// find a/b mod modulo
// find b ^ (modulo - 2)
long long inverse = binaryExponentiation(b, modulo - 2);
return ((inverse * a) % modulo);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, k;
cin >> n >> k;
long long answer = n + 1;
for (int i = 0; i < k; i++) {
answer *= n;
answer %= modulo;
}
if (answer % 2 == 0) {
answer /= 2;
} else {
answer = (answer + modulo) / 2;
}
if (k % 2 == 1) {
cout << answer << "\n";
} else {
long long factorial1 = 1;
for (int i = (k/2) + 1; i <= k; i++) {
factorial1 *= i;
factorial1 %= modulo;
}
long long factorial2 = 1;
for (int i = 1; i <= (k/2); i++) {
factorial2 *= i;
factorial2 %= modulo;
}
long long combination = factorial1;
combination = divide(combination, factorial2);
long long value = 0;
for (int i = 1; i < n; i++) {
long long tmp = binaryExponentiation(i, k/2);
tmp *= binaryExponentiation(n - i, k/2);
tmp %= modulo;
tmp *= combination;
tmp %= modulo;
value += tmp;
value %= modulo;
}
if (value % 2 == 0) {
value /= 2;
} else {
value = (value + modulo) / 2;
}
answer -= value;
answer %= modulo;
if (answer < 0) {
answer += modulo;
}
cout << answer << "\n";
}
return 0;
}
詳細信息
Test #1:
score: 100
Accepted
time: 1ms
memory: 3400kb
input:
3 2
output:
14
result:
ok 1 number(s): "14"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3436kb
input:
5 3
output:
375
result:
ok 1 number(s): "375"
Test #3:
score: 0
Accepted
time: 0ms
memory: 3456kb
input:
2 2
output:
5
result:
ok 1 number(s): "5"
Test #4:
score: 0
Accepted
time: 0ms
memory: 3524kb
input:
10 9
output:
508778235
result:
ok 1 number(s): "508778235"
Test #5:
score: 0
Accepted
time: 1ms
memory: 3604kb
input:
69 3
output:
11497815
result:
ok 1 number(s): "11497815"
Test #6:
score: 0
Accepted
time: 2ms
memory: 3428kb
input:
994 515
output:
33689623
result:
ok 1 number(s): "33689623"
Test #7:
score: 0
Accepted
time: 3ms
memory: 3564kb
input:
4476 6182
output:
114894183
result:
ok 1 number(s): "114894183"
Test #8:
score: 0
Accepted
time: 0ms
memory: 3448kb
input:
58957 12755
output:
932388891
result:
ok 1 number(s): "932388891"
Test #9:
score: 0
Accepted
time: 98ms
memory: 3608kb
input:
218138 28238
output:
392861201
result:
ok 1 number(s): "392861201"
Test #10:
score: 0
Accepted
time: 292ms
memory: 3448kb
input:
644125 316810
output:
420621854
result:
ok 1 number(s): "420621854"
Test #11:
score: 0
Accepted
time: 281ms
memory: 3456kb
input:
612914 505428
output:
973686286
result:
ok 1 number(s): "973686286"
Test #12:
score: 0
Accepted
time: 5ms
memory: 3384kb
input:
998216 938963
output:
251335926
result:
ok 1 number(s): "251335926"
Test #13:
score: 0
Accepted
time: 5ms
memory: 3436kb
input:
990516 996933
output:
549551960
result:
ok 1 number(s): "549551960"
Test #14:
score: 0
Accepted
time: 467ms
memory: 3448kb
input:
999019 999012
output:
637189128
result:
ok 1 number(s): "637189128"
Test #15:
score: 0
Accepted
time: 455ms
memory: 3432kb
input:
999928 999950
output:
185229465
result:
ok 1 number(s): "185229465"
Test #16:
score: 0
Accepted
time: 7ms
memory: 3360kb
input:
999999 999999
output:
384164916
result:
ok 1 number(s): "384164916"
Test #17:
score: 0
Accepted
time: 451ms
memory: 3608kb
input:
999999 1000000
output:
696165930
result:
ok 1 number(s): "696165930"
Test #18:
score: 0
Accepted
time: 7ms
memory: 3440kb
input:
1000000 999999
output:
219071706
result:
ok 1 number(s): "219071706"
Test #19:
score: 0
Accepted
time: 449ms
memory: 3608kb
input:
1000000 1000000
output:
128206597
result:
ok 1 number(s): "128206597"
Test #20:
score: 0
Accepted
time: 1ms
memory: 3440kb
input:
2 10
output:
1410
result:
ok 1 number(s): "1410"
Test #21:
score: 0
Accepted
time: 0ms
memory: 3524kb
input:
84 16
output:
297627153
result:
ok 1 number(s): "297627153"
Test #22:
score: 0
Accepted
time: 1ms
memory: 3428kb
input:
643 800
output:
489237163
result:
ok 1 number(s): "489237163"
Test #23:
score: 0
Accepted
time: 5ms
memory: 3564kb
input:
9903 880
output:
595167333
result:
ok 1 number(s): "595167333"
Test #24:
score: 0
Accepted
time: 46ms
memory: 3548kb
input:
97446 89750
output:
410205549
result:
ok 1 number(s): "410205549"
Test #25:
score: 0
Accepted
time: 89ms
memory: 3376kb
input:
186460 646474
output:
32638530
result:
ok 1 number(s): "32638530"
Test #26:
score: 0
Accepted
time: 232ms
memory: 3436kb
input:
508940 244684
output:
598321755
result:
ok 1 number(s): "598321755"
Test #27:
score: 0
Accepted
time: 266ms
memory: 3456kb
input:
583646 557758
output:
858695621
result:
ok 1 number(s): "858695621"
Test #28:
score: 0
Accepted
time: 445ms
memory: 3440kb
input:
969610 992608
output:
256683498
result:
ok 1 number(s): "256683498"
Test #29:
score: 0
Accepted
time: 465ms
memory: 3452kb
input:
995106 996434
output:
411791999
result:
ok 1 number(s): "411791999"
Test #30:
score: 0
Accepted
time: 455ms
memory: 3456kb
input:
999961 999872
output:
61222370
result:
ok 1 number(s): "61222370"
Test #31:
score: 0
Accepted
time: 464ms
memory: 3432kb
input:
999977 999908
output:
831096762
result:
ok 1 number(s): "831096762"
Test #32:
score: 0
Accepted
time: 460ms
memory: 3568kb
input:
999992 999998
output:
562977678
result:
ok 1 number(s): "562977678"
Test #33:
score: 0
Accepted
time: 430ms
memory: 3448kb
input:
1000000 2
output:
118436113
result:
ok 1 number(s): "118436113"
Test #34:
score: 0
Accepted
time: 10ms
memory: 3440kb
input:
2 1000000
output:
298823641
result:
ok 1 number(s): "298823641"