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QOJ
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 |
---|---|---|---|---|---|---|---|---|---|
#500703 | #6417. Classical Summation Problem | ucup-team2307# | AC ✓ | 161ms | 19336kb | C++20 | 1.4kb | 2024-08-01 18:18:03 | 2024-08-01 18:18:07 |
Judging History
answer
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx,avx2,sse,sse2")
#include<bits/stdc++.h>
#define all(x) begin(x), end(x)
using namespace std;
using ll = long long;
const int N = 2e6 + 66, mod = 998244353;
int fact[N], ifact[N];
void calc() {
ifact[0] = fact[0] = ifact[1] = 1;
for(int i = 2; i < N; i++) {
ifact[i] = mod - (mod / i) * 1ll * ifact[mod % i] % mod;
}
for(int i = 1; i < N; i++) {
fact[i] = fact[i - 1] * 1ll * i % mod;
ifact[i] = ifact[i - 1] * 1ll * ifact[i] % mod;
}
}
int nck(int n, int k) {
if(k < 0 || k > n) return 0;
int ans = fact[n] * 1ll * ifact[k] % mod;
return ans * 1ll * ifact[n-k]%mod;
}
int bp(int a, int p) {
int r = 1;
for(; p; p>>=1, a = a*1ll*a%mod)
if(p&1) r = r*1ll*a%mod;
return r;
}
main() {
cin.tie(0)->sync_with_stdio(0);
//E[med] = sum_{x=0...inf} P[med > x] = sum_k=...n/2-1 P[cnt_(<=x) = k]
calc();
int n, k;
cin >> n >> k;
if(k & 1) {
ll ans = bp(n, k) * 1ll * (n + 1) % mod;
ans = ans * 1ll * ((mod+1)/2) % mod;
cout << ans << '\n';
return 0;
}
ll exp_diff = 0;
for(int i = 1; i < n; i++) {
exp_diff += bp(i, k/2)*1ll*bp(n-i, k/2) % mod;
}
exp_diff = (exp_diff % mod) * 1ll * nck(k, k/2) % mod;
ll exp_sum = (n + 1) * 1ll * bp(n, k) % mod;
ll smoll = (mod + exp_sum - exp_diff) * 1ll * ((mod+1)/2) % mod;
cout << smoll << '\n';
}/*
2 piles sum <= 2
0 0
0 1
0 2
1 1
*/
详细
Test #1:
score: 100
Accepted
time: 11ms
memory: 19240kb
input:
3 2
output:
14
result:
ok 1 number(s): "14"
Test #2:
score: 0
Accepted
time: 17ms
memory: 19332kb
input:
5 3
output:
375
result:
ok 1 number(s): "375"
Test #3:
score: 0
Accepted
time: 15ms
memory: 19312kb
input:
2 2
output:
5
result:
ok 1 number(s): "5"
Test #4:
score: 0
Accepted
time: 11ms
memory: 19240kb
input:
10 9
output:
508778235
result:
ok 1 number(s): "508778235"
Test #5:
score: 0
Accepted
time: 15ms
memory: 19180kb
input:
69 3
output:
11497815
result:
ok 1 number(s): "11497815"
Test #6:
score: 0
Accepted
time: 19ms
memory: 19256kb
input:
994 515
output:
33689623
result:
ok 1 number(s): "33689623"
Test #7:
score: 0
Accepted
time: 10ms
memory: 19260kb
input:
4476 6182
output:
114894183
result:
ok 1 number(s): "114894183"
Test #8:
score: 0
Accepted
time: 15ms
memory: 19256kb
input:
58957 12755
output:
932388891
result:
ok 1 number(s): "932388891"
Test #9:
score: 0
Accepted
time: 36ms
memory: 19164kb
input:
218138 28238
output:
392861201
result:
ok 1 number(s): "392861201"
Test #10:
score: 0
Accepted
time: 101ms
memory: 19216kb
input:
644125 316810
output:
420621854
result:
ok 1 number(s): "420621854"
Test #11:
score: 0
Accepted
time: 97ms
memory: 19240kb
input:
612914 505428
output:
973686286
result:
ok 1 number(s): "973686286"
Test #12:
score: 0
Accepted
time: 15ms
memory: 19184kb
input:
998216 938963
output:
251335926
result:
ok 1 number(s): "251335926"
Test #13:
score: 0
Accepted
time: 15ms
memory: 19332kb
input:
990516 996933
output:
549551960
result:
ok 1 number(s): "549551960"
Test #14:
score: 0
Accepted
time: 154ms
memory: 19332kb
input:
999019 999012
output:
637189128
result:
ok 1 number(s): "637189128"
Test #15:
score: 0
Accepted
time: 159ms
memory: 19244kb
input:
999928 999950
output:
185229465
result:
ok 1 number(s): "185229465"
Test #16:
score: 0
Accepted
time: 18ms
memory: 19236kb
input:
999999 999999
output:
384164916
result:
ok 1 number(s): "384164916"
Test #17:
score: 0
Accepted
time: 150ms
memory: 19240kb
input:
999999 1000000
output:
696165930
result:
ok 1 number(s): "696165930"
Test #18:
score: 0
Accepted
time: 19ms
memory: 19200kb
input:
1000000 999999
output:
219071706
result:
ok 1 number(s): "219071706"
Test #19:
score: 0
Accepted
time: 150ms
memory: 19180kb
input:
1000000 1000000
output:
128206597
result:
ok 1 number(s): "128206597"
Test #20:
score: 0
Accepted
time: 19ms
memory: 19264kb
input:
2 10
output:
1410
result:
ok 1 number(s): "1410"
Test #21:
score: 0
Accepted
time: 18ms
memory: 19272kb
input:
84 16
output:
297627153
result:
ok 1 number(s): "297627153"
Test #22:
score: 0
Accepted
time: 14ms
memory: 19204kb
input:
643 800
output:
489237163
result:
ok 1 number(s): "489237163"
Test #23:
score: 0
Accepted
time: 14ms
memory: 19184kb
input:
9903 880
output:
595167333
result:
ok 1 number(s): "595167333"
Test #24:
score: 0
Accepted
time: 26ms
memory: 19332kb
input:
97446 89750
output:
410205549
result:
ok 1 number(s): "410205549"
Test #25:
score: 0
Accepted
time: 44ms
memory: 19204kb
input:
186460 646474
output:
32638530
result:
ok 1 number(s): "32638530"
Test #26:
score: 0
Accepted
time: 82ms
memory: 19248kb
input:
508940 244684
output:
598321755
result:
ok 1 number(s): "598321755"
Test #27:
score: 0
Accepted
time: 96ms
memory: 19256kb
input:
583646 557758
output:
858695621
result:
ok 1 number(s): "858695621"
Test #28:
score: 0
Accepted
time: 151ms
memory: 19176kb
input:
969610 992608
output:
256683498
result:
ok 1 number(s): "256683498"
Test #29:
score: 0
Accepted
time: 154ms
memory: 19264kb
input:
995106 996434
output:
411791999
result:
ok 1 number(s): "411791999"
Test #30:
score: 0
Accepted
time: 150ms
memory: 19236kb
input:
999961 999872
output:
61222370
result:
ok 1 number(s): "61222370"
Test #31:
score: 0
Accepted
time: 161ms
memory: 19336kb
input:
999977 999908
output:
831096762
result:
ok 1 number(s): "831096762"
Test #32:
score: 0
Accepted
time: 160ms
memory: 19248kb
input:
999992 999998
output:
562977678
result:
ok 1 number(s): "562977678"
Test #33:
score: 0
Accepted
time: 24ms
memory: 19316kb
input:
1000000 2
output:
118436113
result:
ok 1 number(s): "118436113"
Test #34:
score: 0
Accepted
time: 15ms
memory: 19184kb
input:
2 1000000
output:
298823641
result:
ok 1 number(s): "298823641"