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 |
---|---|---|---|---|---|---|---|---|---|
#149803 | #286. 集合 | dcyt | 100 | 9470ms | 234364kb | C++11 | 1.8kb | 2022-07-22 11:53:57 | 2022-07-22 13:34:28 |
answer
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/hash_policy.hpp>
#define fi first
#define se second
using namespace std;
using namespace __gnu_pbds;
using ll = long long;
using db = double;
using pii = pair<int, int>;
using pil = pair<int, ll>;
mt19937 rnd(chrono::system_clock::now().time_since_epoch().count());
const int N = 1e7 + 5;
const ll P = 998244353;
ll qpow(ll a, ll b)
{
ll res = 1;
for (; b; b >>= 1, a = a * a % P)
if (b & 1) res = res * a % P;
return res;
}
ll fac[N], ivf[N];
void init(int n)
{
fac[0] = 1;
for (int i = 1; i <= n; i++)
fac[i] = fac[i - 1] * i % P;
ivf[n] = qpow(fac[n], P - 2);
for (int i = n - 1; i >= 0; i--)
ivf[i] = ivf[i + 1] * (i + 1) % P;
}
ll C(int n, int m)
{
return n < m ? 0 : fac[n] * ivf[m] % P * ivf[n - m] % P;
}
ll n, t;
int k;
ll ans[N];
int main()
{
init(1e7);
scanf("%lld%d%lld", &n, &k, &t);
if (t == 1)
{
puts("1");
return 0;
}
ll it1 = qpow((t + P - 1) % P, P - 2);
ans[1] = (qpow(t, n + 1) + P - t) % P * it1 % P;
ll C = n, C1 = 1, C2 = 1;
for (int i = 2; i <= k; i++)
{
ll c1 = 0, c2 = 0;
if (n >= i) C = C * (n - i + 1) % P;
else C = 0;
if (n - 1 >= i - 1) c1 = C1 = C1 * ((n - 1) - (i - 1) + 1) % P;
else C1 = 0;
if (i == 2) c2 = 1;
else if (n - 1 >= i - 2) c2 = C2 = C2 * ((n - 1) - (i - 2) + 1) % P;
else C2 = 0;
c1 = c1 * ivf[i - 1] % P;
c2 = c2 * ivf[i - 2] % P;
ans[i] = (ans[i - 1] + (P - c1) * t % P + (P - c2) * t % P) % P * it1 % P;
}
C = C * ivf[k] % P;
printf("%lld\n", ans[k] * qpow(C, P - 2) % P);
}
详细
小提示:点击横条可展开更详细的信息
Subtask #1:
score: 10
Accepted
Test #1:
score: 10
Accepted
time: 103ms
memory: 157436kb
input:
974358060 9789202 1
output:
1
result:
ok 1 number(s): "1"
Test #2:
score: 0
Accepted
time: 109ms
memory: 157436kb
input:
974374867 9782669 1
output:
1
result:
ok 1 number(s): "1"
Test #3:
score: 0
Accepted
time: 123ms
memory: 157436kb
input:
974391674 9257635 1
output:
1
result:
ok 1 number(s): "1"
Test #4:
score: 0
Accepted
time: 105ms
memory: 157440kb
input:
974408481 9732602 1
output:
1
result:
ok 1 number(s): "1"
Test #5:
score: 0
Accepted
time: 102ms
memory: 157436kb
input:
974425288 9207568 1
output:
1
result:
ok 1 number(s): "1"
Test #6:
score: 0
Accepted
time: 111ms
memory: 157440kb
input:
974442095 9682535 1
output:
1
result:
ok 1 number(s): "1"
Test #7:
score: 0
Accepted
time: 126ms
memory: 157440kb
input:
974458902 9157501 1
output:
1
result:
ok 1 number(s): "1"
Test #8:
score: 0
Accepted
time: 139ms
memory: 157436kb
input:
974475709 9632468 1
output:
1
result:
ok 1 number(s): "1"
Test #9:
score: 0
Accepted
time: 111ms
memory: 157440kb
input:
974492516 9625935 1
output:
1
result:
ok 1 number(s): "1"
Test #10:
score: 0
Accepted
time: 113ms
memory: 157436kb
input:
974509323 9100901 1
output:
1
result:
ok 1 number(s): "1"
Subtask #2:
score: 30
Accepted
Test #11:
score: 30
Accepted
time: 132ms
memory: 164140kb
input:
939830 855862 952890428
output:
769580874
result:
ok 1 number(s): "769580874"
Test #12:
score: 0
Accepted
time: 131ms
memory: 164824kb
input:
956637 943184 988243671
output:
729644598
result:
ok 1 number(s): "729644598"
Test #13:
score: 0
Accepted
time: 111ms
memory: 164436kb
input:
973444 893280 974942969
output:
376458332
result:
ok 1 number(s): "376458332"
Test #14:
score: 0
Accepted
time: 132ms
memory: 164632kb
input:
990251 918400 910471776
output:
601893966
result:
ok 1 number(s): "601893966"
Test #15:
score: 0
Accepted
time: 112ms
memory: 164376kb
input:
907057 885478 996995510
output:
279439643
result:
ok 1 number(s): "279439643"
Test #16:
score: 0
Accepted
time: 120ms
memory: 164448kb
input:
923864 894832 932524317
output:
754485259
result:
ok 1 number(s): "754485259"
Test #17:
score: 0
Accepted
time: 134ms
memory: 164176kb
input:
940671 859705 919223615
output:
735360983
result:
ok 1 number(s): "735360983"
Test #18:
score: 0
Accepted
time: 132ms
memory: 164608kb
input:
957478 915557 954576858
output:
846297917
result:
ok 1 number(s): "846297917"
Test #19:
score: 0
Accepted
time: 143ms
memory: 164916kb
input:
974285 954471 941276156
output:
519140979
result:
ok 1 number(s): "519140979"
Test #20:
score: 0
Accepted
time: 160ms
memory: 164956kb
input:
991092 960406 927975454
output:
393800468
result:
ok 1 number(s): "393800468"
Subtask #3:
score: 30
Accepted
Test #21:
score: 30
Accepted
time: 371ms
memory: 234364kb
input:
974694200 9844034 2
output:
717614679
result:
ok 1 number(s): "717614679"
Test #22:
score: 0
Accepted
time: 377ms
memory: 233972kb
input:
974727814 9793967 2
output:
903396834
result:
ok 1 number(s): "903396834"
Test #23:
score: 0
Accepted
time: 278ms
memory: 229872kb
input:
974744621 9268933 2
output:
293082936
result:
ok 1 number(s): "293082936"
Test #24:
score: 0
Accepted
time: 288ms
memory: 229820kb
input:
974761428 9262400 2
output:
568471499
result:
ok 1 number(s): "568471499"
Test #25:
score: 0
Accepted
time: 253ms
memory: 229424kb
input:
974795042 9212333 2
output:
174349571
result:
ok 1 number(s): "174349571"
Test #26:
score: 0
Accepted
time: 281ms
memory: 233136kb
input:
974811849 9687300 2
output:
54692201
result:
ok 1 number(s): "54692201"
Test #27:
score: 0
Accepted
time: 313ms
memory: 229040kb
input:
974828656 9162266 2
output:
178547426
result:
ok 1 number(s): "178547426"
Test #28:
score: 0
Accepted
time: 314ms
memory: 232744kb
input:
974845463 9637233 2
output:
848853881
result:
ok 1 number(s): "848853881"
Test #29:
score: 0
Accepted
time: 252ms
memory: 228596kb
input:
974879077 9105666 2
output:
939782679
result:
ok 1 number(s): "939782679"
Test #30:
score: 0
Accepted
time: 259ms
memory: 232308kb
input:
974895884 9580633 2
output:
341052536
result:
ok 1 number(s): "341052536"
Subtask #4:
score: 20
Accepted
Test #31:
score: 20
Accepted
time: 125ms
memory: 164880kb
input:
974912691 950001 982518805
output:
127609714
result:
ok 1 number(s): "127609714"
Test #32:
score: 0
Accepted
time: 129ms
memory: 164660kb
input:
974929498 922425 969218103
output:
988959503
result:
ok 1 number(s): "988959503"
Test #33:
score: 0
Accepted
time: 136ms
memory: 165232kb
input:
974946305 994850 904746910
output:
652493805
result:
ok 1 number(s): "652493805"
Test #34:
score: 0
Accepted
time: 128ms
memory: 164800kb
input:
974979919 939698 926799451
output:
297254489
result:
ok 1 number(s): "297254489"
Test #35:
score: 0
Accepted
time: 112ms
memory: 164584kb
input:
974996726 912122 913498749
output:
3872843
result:
ok 1 number(s): "3872843"
Test #36:
score: 0
Accepted
time: 128ms
memory: 164660kb
input:
975013533 922374 948851992
output:
824700719
result:
ok 1 number(s): "824700719"
Test #37:
score: 0
Accepted
time: 138ms
memory: 165228kb
input:
975030340 994799 935551290
output:
910283886
result:
ok 1 number(s): "910283886"
Test #38:
score: 0
Accepted
time: 137ms
memory: 165012kb
input:
975047147 967223 970904533
output:
524094901
result:
ok 1 number(s): "524094901"
Test #39:
score: 0
Accepted
time: 116ms
memory: 164800kb
input:
975063954 939647 957603831
output:
976518923
result:
ok 1 number(s): "976518923"
Test #40:
score: 0
Accepted
time: 170ms
memory: 164580kb
input:
975080761 912071 944303129
output:
671474890
result:
ok 1 number(s): "671474890"
Subtask #5:
score: 10
Accepted
Test #41:
score: 10
Accepted
time: 305ms
memory: 234008kb
input:
975097568 9798732 979656372
output:
511951684
result:
ok 1 number(s): "511951684"
Test #42:
score: 0
Accepted
time: 263ms
memory: 229904kb
input:
975114375 9273698 966355670
output:
258620932
result:
ok 1 number(s): "258620932"
Test #43:
score: 0
Accepted
time: 299ms
memory: 233616kb
input:
975131182 9748665 901884477
output:
680834727
result:
ok 1 number(s): "680834727"
Test #44:
score: 0
Accepted
time: 288ms
memory: 229464kb
input:
975164796 9217098 923937018
output:
420034109
result:
ok 1 number(s): "420034109"
Test #45:
score: 0
Accepted
time: 249ms
memory: 233172kb
input:
975181603 9692065 910636316
output:
969346798
result:
ok 1 number(s): "969346798"
Test #46:
score: 0
Accepted
time: 273ms
memory: 229072kb
input:
975198410 9167031 945989559
output:
153740899
result:
ok 1 number(s): "153740899"
Test #47:
score: 0
Accepted
time: 247ms
memory: 232788kb
input:
975215217 9641998 932688857
output:
617915726
result:
ok 1 number(s): "617915726"
Test #48:
score: 0
Accepted
time: 289ms
memory: 232392kb
input:
975248831 9591931 954741398
output:
414830040
result:
ok 1 number(s): "414830040"
Test #49:
score: 0
Accepted
time: 267ms
memory: 232340kb
input:
975265638 9585398 990094641
output:
300778334
result:
ok 1 number(s): "300778334"
Test #50:
score: 0
Accepted
time: 236ms
memory: 228240kb
input:
975282445 9060364 976793939
output:
153955626
result:
ok 1 number(s): "153955626"