QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#101339 | #5031. 核 | zhoukangyang | 30 | 1764ms | 22936kb | C++17 | 3.5kb | 2023-04-29 10:41:19 | 2023-04-29 10:41:22 |
Judging History
answer
#include<bits/stdc++.h>
#define L(i, j, k) for(int i = (j); i <= (k); ++i)
#define R(i, j, k) for(int i = (j); i >= (k); --i)
#define ll long long
#define vi vector <int>
#define sz(a) ((int) (a).size())
#define me(f, x) memset(f, x, sizeof(f))
#define uint unsigned int
#define ull unsigned long long
#define bs bitset < N >
using namespace std;
const int N = 1e6 + 7;
int n, q, mod;
int pw[N], fac[N], ifac[N];
int qpow(int x, int y = mod - 2) {
int res = 1;
for(; y; x = (ll) x * x % mod, y >>= 1) if(y & 1) res = (ll) res * x % mod;
return res;
}
void q_init(int x) {
pw[0] = 1;
L(i, 1, x) pw[i] = (ll) pw[i - 1] * q % mod;
L(i, 1, x) fac[i] = pw[i] - 1;
fac[0] = ifac[0] = 1;
L(i, 1, x)
ifac[i] = (ll) qpow (fac[i]) * ifac[i - 1] % mod,
fac[i] = (ll) fac[i - 1] * fac[i] % mod;
}
int q_C(int x, int y) {
return x < y || y < 0 ? 0 : (ll) fac[x] * ifac[y] % mod * ifac[x - y] % mod;
}
inline int sgn(int x) {
return (x & 1) ? mod - 1 : 1;
}
template < int L, int K > struct DBM {
static const int R = (L + 1) * (K + 1);
int lpos, a[R * 10 + 7];
int G[R + 7][R + 7], cur[R + 7], ns[R + 7];
int f[L + 2][K + 2], id[L + 2][K + 2], idt;
inline void insert() {
R(i, idt, 1) if(cur[i]) {
if(!G[i][i]) {
L(j, 1, i)
G[i][j] = cur[j];
}
int iv = (ll) (mod - cur[i]) * qpow(G[i][i]) % mod;
L(j, 1, i)
(cur[j] += (ll) iv * G[i][j] % mod) %= mod;
}
}
void gauss(int *a, int n, int lpos = 0) {
n = min(n, R * 10), idt = 0;
L(i, 0, L)
L(j, 0, K)
id[i][j] = ++idt;
L(i, L + 1, n) {
L(j, 0, idt)
cur[j] = 0;
L(x, 0, L) if(x < i) {
int pw = a[i - x];
L(y, 0, K)
cur[id[x][y]] = pw,
pw = (ll) pw * ::pw[lpos + i] % mod;
}
insert();
}
int pos = 1;
while(G[pos][pos]) ++pos;
ns[pos] = 1;
if(pos > idt) {
cout << "TAT" << endl;
exit(0);
}
L(i, pos + 1, idt) {
int s = 0;
L(j, 1, i - 1) {
(s += (ll) G[i][j] * ns[j] % mod) %= mod;
}
ns[i] = (ll) (mod - s) * qpow(G[i][i]) % mod;
}
L(i, 0, L)
L(j, 0, K)
f[i][j] = ns[id[i][j]];
L(i, L + 1, n) {
L(j, 0, idt)
cur[j] = 0;
int s = 0;
L(x, 0, L) if(x < i) {
int pw = a[i - x];
L(y, 0, K)
(s += (ll) pw * f[x][y] % mod) %= mod,
pw = (ll) pw * ::pw[lpos + i] % mod;
}
}
}
};
DBM < 2, 3 > S;
const int T = 80;
int f[N], g[N], ans[N];
int main() {
ios :: sync_with_stdio(false);
cin.tie(0); cout.tie(0);
cin >> n >> q >> mod;
q_init(n + 1);
int mn = min(n, T);
f[0] = 1;
L(i, 1, mn) {
f[i] = (ll) f[i - 1] * (pw[n] + mod - pw[n - i]) % mod;
}
L(i, 0, mn) {
g[i] = (ll) sgn(i) * qpow(q, i * (i - 1) / 2) % mod;
}
L(i, 0, mn) {
L(j, 0, mn - i) {
(ans[i + j] += (ll) q_C(i + j, i) * f[i] % mod * g[j] % mod) %= mod;
}
}
S.gauss(ans, T);
L(i, T + 1, n) {
int s = 0;
L(x, 1, 2) {
int pw = ans[i - x];
L(y, 0, 3)
(s += (ll) pw * S.f[x][y] % mod) %= mod, pw = (ll) pw * ::pw[i] % mod;
}
int fs = 0, pw = 1;
L(y, 0, 3)
(fs += (ll) pw * S.f[0][y] % mod) %= mod, pw = (ll) pw * ::pw[i] % mod;
ans[i] = (ll) (mod - s) * qpow(fs) % mod;
}
L(i, 0, n) {
f[i] = ans[i];
}
L(i, 0, n) {
f[i] = (ll) f[i] * q_C(n, i) % mod;
}
int pw = 1;
L(i, 1, n) {
pw = (ll) pw * q % (mod - 1);
}
int s = 1, ns = 0;
R(i, n, 0) {
(ns += (ll) f[i] * qpow(3, s) % mod) %= mod;
s = (ll) s * pw % (mod - 1);
}
cout << ns << '\n';
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Subtask #1:
score: 10
Accepted
Test #1:
score: 10
Accepted
time: 0ms
memory: 3412kb
input:
1 2 540053233
output:
9
result:
ok 1 number(s): "9"
Test #2:
score: 0
Accepted
time: 2ms
memory: 3536kb
input:
2 2 156542707
output:
43046970
result:
ok 1 number(s): "43046970"
Test #3:
score: 0
Accepted
time: 2ms
memory: 3440kb
input:
1 2 186225229
output:
9
result:
ok 1 number(s): "9"
Test #4:
score: 0
Accepted
time: 0ms
memory: 3540kb
input:
3 3 109884329
output:
100602209
result:
ok 1 number(s): "100602209"
Test #5:
score: 0
Accepted
time: 2ms
memory: 3488kb
input:
1 2 144802297
output:
9
result:
ok 1 number(s): "9"
Subtask #2:
score: 0
Wrong Answer
Dependency #1:
100%
Accepted
Test #6:
score: 0
Wrong Answer
time: 2ms
memory: 3488kb
input:
20 21992843 328859143
output:
TAT
result:
wrong output format Expected integer, but "TAT" found
Subtask #3:
score: 0
Skipped
Dependency #2:
0%
Subtask #4:
score: 20
Accepted
Test #26:
score: 20
Accepted
time: 1764ms
memory: 22936kb
input:
998818 198334853 998244353
output:
153251445
result:
ok 1 number(s): "153251445"
Test #27:
score: 0
Accepted
time: 1618ms
memory: 21348kb
input:
914379 128814383 998244353
output:
477606145
result:
ok 1 number(s): "477606145"
Test #28:
score: 0
Accepted
time: 1663ms
memory: 21824kb
input:
944474 478445339 998244353
output:
174204073
result:
ok 1 number(s): "174204073"
Test #29:
score: 0
Accepted
time: 1695ms
memory: 22008kb
input:
948637 711592127 998244353
output:
178256114
result:
ok 1 number(s): "178256114"
Test #30:
score: 0
Accepted
time: 1627ms
memory: 21492kb
input:
927564 14465663 998244353
output:
315244613
result:
ok 1 number(s): "315244613"
Test #31:
score: 0
Accepted
time: 1654ms
memory: 21684kb
input:
934615 392799073 998244353
output:
892700270
result:
ok 1 number(s): "892700270"
Test #32:
score: 0
Accepted
time: 1595ms
memory: 21296kb
input:
917196 124972031 998244353
output:
782017412
result:
ok 1 number(s): "782017412"
Test #33:
score: 0
Accepted
time: 1704ms
memory: 22140kb
input:
957149 392606173 998244353
output:
159348443
result:
ok 1 number(s): "159348443"
Test #34:
score: 0
Accepted
time: 1756ms
memory: 22852kb
input:
997042 184649453 998244353
output:
464643024
result:
ok 1 number(s): "464643024"
Test #35:
score: 0
Accepted
time: 1758ms
memory: 21968kb
input:
953353 14071961 998244353
output:
391688875
result:
ok 1 number(s): "391688875"
Subtask #5:
score: 0
Runtime Error
Test #36:
score: 0
Runtime Error
input:
9909956 720431399 720431401
output:
result:
Subtask #6:
score: 0
Skipped
Dependency #1:
100%
Accepted
Dependency #2:
0%