QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#103067 | #6323. Range NEQ | wsyear | AC ✓ | 103ms | 23132kb | C++14 | 8.5kb | 2023-05-04 11:34:56 | 2023-05-04 11:34:57 |
Judging History
answer
/*
* Author: Enucai
* Date: 2022-12-14 08:47:28
* LastEditTime: 2023-05-04 11:34:52
*/
#include <bits/stdc++.h>
#include <sys/time.h>
#ifdef dbg
#define D(...) fprintf(stderr, __VA_ARGS__)
#define DD(...) D(#__VA_ARGS__ " = "), debug_helper::debug(__VA_ARGS__), D("\n")
#include "C:\Users\wsyear\Desktop\OI\templates\debug.hpp"
#else
#define D(...) ((void)0)
#define DD(...) ((void)0)
#endif
#define rep(i, j, k) for (int i = (j); i <= (k); ++i)
#define per(i, j, k) for (int i = (j); i >= (k); --i)
#define SZ(v) int((v).size())
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
#define gc getchar
#define pc putchar
using ll = long long;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;
using namespace std;
template <class T = int> T read() {
T x = 0; bool f = 0; char ch = gc();
while (!isdigit(ch)) f = ch == '-', ch = gc();
while (isdigit(ch)) x = (x << 3) + (x << 1) + (ch ^ 48), ch = gc();
return f ? -x: x;
}
template <class T> void write(T x) {
if (x >= 0) { if (x > 9) write(x / 10); pc(x % 10 + 48); }
else { pc('-'); if (x < -9) write(-x / 10); pc(48 - x % 10); }
}
template <int P>
class mod_int {
using Z = mod_int;
private:
static int mo(int x) { return x < 0 ? x + P : x; }
public:
int x;
int val() const { return x; }
mod_int() : x(0) {}
template <class T>
mod_int(const T &x_) : x(x_ >= 0 && x_ < P ? static_cast<int>(x_) : mo(static_cast<int>(x_ % P))) {}
bool operator==(const Z &rhs) const { return x == rhs.x; }
bool operator!=(const Z &rhs) const { return x != rhs.x; }
Z operator-() const { return Z(x ? P - x : 0); }
Z pow(long long k) const {
Z res = 1, t = *this;
while (k) {
if (k & 1) res *= t;
if (k >>= 1) t *= t;
}
return res;
}
Z &operator++() {
x < P - 1 ? ++x : x = 0;
return *this;
}
Z &operator--() {
x ? --x : x = P - 1;
return *this;
}
Z operator++(int) {
Z ret = x;
x < P - 1 ? ++x : x = 0;
return ret;
}
Z operator--(int) {
Z ret = x;
x ? --x : x = P - 1;
return ret;
}
Z inv() const { return pow(P - 2); }
Z &operator+=(const Z &rhs) {
(x += rhs.x) >= P && (x -= P);
return *this;
}
Z &operator-=(const Z &rhs) {
(x -= rhs.x) < 0 && (x += P);
return *this;
}
Z &operator*=(const Z &rhs) {
x = 1ULL * x * rhs.x % P;
return *this;
}
Z &operator/=(const Z &rhs) { return *this *= rhs.inv(); }
#define setO(T, o) \
friend T operator o(const Z &lhs, const Z &rhs) {\
Z res = lhs; \
return res o## = rhs; \
}
setO(Z, +) setO(Z, -) setO(Z, *) setO(Z, /)
#undef setO
};
const int P = 998244353;
using Z = mod_int<P>;
namespace Poly_space {
std::vector<int> rev;
std::vector<Z> roots{0, 1};
void dft(std::vector<Z> &a) {
int n = a.size();
if (int(rev.size()) != n) {
int k = __builtin_ctz(n) - 1;
rev.resize(n);
for (int i = 0; i < n; i++) {
rev[i] = rev[i >> 1] >> 1 | (i & 1 ? 1 << k : 0);
}
}
for (int i = 0; i < n; i++)
if (rev[i] < i) std::swap(a[i], a[rev[i]]);
if (int(roots.size()) < n) {
int k = __builtin_ctz(roots.size());
roots.resize(n);
while ((1 << k) < n) {
Z e = Z(3).pow((P - 1) >> (k + 1));
for (int i = 1 << (k - 1); i < (1 << k); i++)
roots[2 * i] = roots[i], roots[2 * i + 1] = roots[i] * e;
k++;
}
}
for (int k = 1; k < n; k *= 2)
for (int i = 0; i < n; i += 2 * k)
for (int j = 0; j < k; j++) {
Z u = a[i + j], v = a[i + j + k] * roots[k + j];
a[i + j] = u + v, a[i + j + k] = u - v;
}
}
void idft(std::vector<Z> &a) {
int n = a.size();
std::reverse(a.begin() + 1, a.end());
dft(a);
Z inv = (1 - P) / n;
for (int i = 0; i < n; i++) a[i] *= inv;
}
struct Poly {
std::vector<Z> a;
Poly() {}
Poly(const std::vector<Z> &a) : a(a) {}
Poly(const std::initializer_list<Z> &a) : a(a) {}
int size() const { return a.size(); }
void resize(int n) { a.resize(n); }
Z operator[](int idx) const {
if (idx < 0 || idx >= size()) return 0;
return a[idx];
}
Z &operator[](int idx) { return a[idx]; }
Poly mulxk(int k) const {
auto b = a;
b.insert(b.begin(), k, 0);
return Poly(b);
}
Poly modxk(int k) const {
k = std::min(k, size());
return Poly(std::vector<Z>(a.begin(), a.begin() + k));
}
Poly divxk(int k) const {
if (size() <= k) return Poly();
return Poly(std::vector<Z>(a.begin() + k, a.end()));
}
friend Poly operator+(const Poly &a, const Poly &b) {
std::vector<Z> res(std::max(a.size(), b.size()));
for (int i = 0; i < int(res.size()); i++) res[i] = a[i] + b[i];
return Poly(res);
}
friend Poly operator-(const Poly &a, const Poly &b) {
std::vector<Z> res(std::max(a.size(), b.size()));
for (int i = 0; i < int(res.size()); i++) res[i] = a[i] - b[i];
return Poly(res);
}
friend Poly operator*(Poly a, Poly b) {
if (a.size() == 0 || b.size() == 0) return Poly();
int sz = 1, tot = a.size() + b.size() - 1;
while (sz < tot) sz *= 2;
a.a.resize(sz), b.a.resize(sz), dft(a.a), dft(b.a);
for (int i = 0; i < sz; ++i) a.a[i] = a[i] * b[i];
idft(a.a), a.resize(tot);
return a;
}
friend Poly operator*(Z a, Poly b) {
for (int i = 0; i < int(b.size()); i++) b[i] *= a;
return b;
}
friend Poly operator*(Poly a, Z b) {
for (int i = 0; i < int(a.size()); i++) a[i] *= b;
return a;
}
Poly &operator+=(Poly b) { return (*this) = (*this) + b; }
Poly &operator-=(Poly b) { return (*this) = (*this) - b; }
Poly &operator*=(Poly b) { return (*this) = (*this) * b; }
Poly deriv() const {
if (a.empty()) return Poly();
std::vector<Z> res(size() - 1);
for (int i = 0; i < size() - 1; ++i) res[i] = (i + 1) * a[i + 1];
return Poly(res);
}
Poly integr() const {
std::vector<Z> res(size() + 1);
for (int i = 0; i < size(); ++i) res[i + 1] = a[i] / (i + 1);
return Poly(res);
}
Poly inv(int m) const {
Poly x{a[0].inv()};
int k = 1;
while (k < m) k *= 2, x = (x * (Poly{2} - modxk(k) * x)).modxk(k);
return x.modxk(m);
}
Poly log(int m) const {
return (deriv() * inv(m)).integr().modxk(m);
}
Poly exp(int m) const {
Poly x{1};
int k = 1;
while (k < m) k *= 2, x = (x * (Poly{1} - x.log(k) + modxk(k))).modxk(k);
return x.modxk(m);
}
Poly sqrt(int m) const {
Poly x{1};
int k = 1;
while (k < m) k *= 2, x = (x + (modxk(k) * x.inv(k)).modxk(k)) * ((P + 1) / 2);
return x.modxk(m);
}
Poly mulT(Poly b) const {
if (b.size() == 0) return Poly();
int n = b.size();
std::reverse(b.a.begin(), b.a.end());
return ((*this) * b).divxk(n - 1);
}
std::vector<Z> eval(std::vector<Z> x) const {
if (size() == 0) return std::vector<Z>(x.size(), 0);
const int n = std::max(int(x.size()), size());
std::vector<Poly> q(4 * n);
std::vector<Z> ans(x.size());
x.resize(n);
std::function<void(int, int, int)> build = [&](int p, int l, int r) {
if (r - l == 1) q[p] = Poly{1, -x[l]};
else {
int m = (l + r) / 2;
build(2 * p, l, m), build(2 * p + 1, m, r);
q[p] = q[2 * p] * q[2 * p + 1];
}
};
build(1, 0, n);
std::function<void(int, int, int, const Poly &)> work = [&](int p, int l, int r, const Poly &num) {
if (r - l == 1) {
if (l < int(ans.size())) ans[l] = num[0];
} else {
int m = (l + r) / 2;
work(2 * p, l, m, num.mulT(q[2 * p + 1]).modxk(m - l));
work(2 * p + 1, m, r, num.mulT(q[2 * p]).modxk(r - m));
}
};
work(1, 0, n, mulT(q[1].inv(n)));
return ans;
}
};
}
using namespace Poly_space;
const int N = 1000010;
int n, m;
Z fac[N], ivf[N];
Z binom(int x, int y) {
if (x < 0 || y < 0 || x < y) return 0;
return fac[x] * ivf[y] * ivf[x - y];
}
int main() {
n = read(), m = read();
fac[0] = 1;
rep (i, 1, n * m) fac[i] = fac[i - 1] * i;
ivf[n * m] = fac[n * m].inv();
per (i, n * m, 1) ivf[i - 1] = ivf[i] * i;
Poly F; F.resize(m + 1);
rep (i, 0, m) F[i] = binom(m, i) * binom(m, i) * fac[i];
rep (i, 0, m) if (i & 1) F[i] = -F[i];
int sz = 1;
while (sz <= n * m) sz <<= 1;
F.resize(sz), dft(F.a);
for (Z &x : F.a) x = x.pow(n);
idft(F.a);
Z ans = 0;
rep (i, 0, n * m) ans += F[i] * fac[n * m - i];
write(ans.val());
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 3ms
memory: 11248kb
input:
2 2
output:
4
result:
ok 1 number(s): "4"
Test #2:
score: 0
Accepted
time: 1ms
memory: 11172kb
input:
5 1
output:
44
result:
ok 1 number(s): "44"
Test #3:
score: 0
Accepted
time: 1ms
memory: 11392kb
input:
167 91
output:
284830080
result:
ok 1 number(s): "284830080"
Test #4:
score: 0
Accepted
time: 3ms
memory: 11244kb
input:
2 1
output:
1
result:
ok 1 number(s): "1"
Test #5:
score: 0
Accepted
time: 2ms
memory: 11292kb
input:
2 3
output:
36
result:
ok 1 number(s): "36"
Test #6:
score: 0
Accepted
time: 3ms
memory: 11188kb
input:
2 4
output:
576
result:
ok 1 number(s): "576"
Test #7:
score: 0
Accepted
time: 7ms
memory: 11192kb
input:
3 1
output:
2
result:
ok 1 number(s): "2"
Test #8:
score: 0
Accepted
time: 3ms
memory: 11236kb
input:
3 2
output:
80
result:
ok 1 number(s): "80"
Test #9:
score: 0
Accepted
time: 1ms
memory: 11188kb
input:
3 3
output:
12096
result:
ok 1 number(s): "12096"
Test #10:
score: 0
Accepted
time: 1ms
memory: 11192kb
input:
3 4
output:
4783104
result:
ok 1 number(s): "4783104"
Test #11:
score: 0
Accepted
time: 2ms
memory: 11188kb
input:
4 1
output:
9
result:
ok 1 number(s): "9"
Test #12:
score: 0
Accepted
time: 3ms
memory: 11248kb
input:
4 2
output:
4752
result:
ok 1 number(s): "4752"
Test #13:
score: 0
Accepted
time: 0ms
memory: 11220kb
input:
4 3
output:
17927568
result:
ok 1 number(s): "17927568"
Test #14:
score: 0
Accepted
time: 3ms
memory: 11224kb
input:
4 4
output:
776703752
result:
ok 1 number(s): "776703752"
Test #15:
score: 0
Accepted
time: 1ms
memory: 11260kb
input:
5 2
output:
440192
result:
ok 1 number(s): "440192"
Test #16:
score: 0
Accepted
time: 0ms
memory: 11224kb
input:
5 3
output:
189125068
result:
ok 1 number(s): "189125068"
Test #17:
score: 0
Accepted
time: 1ms
memory: 11232kb
input:
5 4
output:
975434093
result:
ok 1 number(s): "975434093"
Test #18:
score: 0
Accepted
time: 88ms
memory: 23060kb
input:
1000 1000
output:
720037464
result:
ok 1 number(s): "720037464"
Test #19:
score: 0
Accepted
time: 7ms
memory: 11292kb
input:
72 42
output:
638177567
result:
ok 1 number(s): "638177567"
Test #20:
score: 0
Accepted
time: 0ms
memory: 11244kb
input:
15 19
output:
663050288
result:
ok 1 number(s): "663050288"
Test #21:
score: 0
Accepted
time: 1ms
memory: 11288kb
input:
68 89
output:
94365047
result:
ok 1 number(s): "94365047"
Test #22:
score: 0
Accepted
time: 3ms
memory: 11252kb
input:
92 37
output:
652605307
result:
ok 1 number(s): "652605307"
Test #23:
score: 0
Accepted
time: 1ms
memory: 11348kb
input:
61 87
output:
498277867
result:
ok 1 number(s): "498277867"
Test #24:
score: 0
Accepted
time: 3ms
memory: 11348kb
input:
81 40
output:
133095344
result:
ok 1 number(s): "133095344"
Test #25:
score: 0
Accepted
time: 1ms
memory: 11204kb
input:
7 91
output:
524164813
result:
ok 1 number(s): "524164813"
Test #26:
score: 0
Accepted
time: 1ms
memory: 11196kb
input:
31 18
output:
361233485
result:
ok 1 number(s): "361233485"
Test #27:
score: 0
Accepted
time: 7ms
memory: 11300kb
input:
74 54
output:
500686087
result:
ok 1 number(s): "500686087"
Test #28:
score: 0
Accepted
time: 2ms
memory: 11196kb
input:
32 2
output:
586504335
result:
ok 1 number(s): "586504335"
Test #29:
score: 0
Accepted
time: 45ms
memory: 16952kb
input:
656 718
output:
346764298
result:
ok 1 number(s): "346764298"
Test #30:
score: 0
Accepted
time: 23ms
memory: 13784kb
input:
254 689
output:
358078813
result:
ok 1 number(s): "358078813"
Test #31:
score: 0
Accepted
time: 50ms
memory: 16952kb
input:
713 674
output:
914437613
result:
ok 1 number(s): "914437613"
Test #32:
score: 0
Accepted
time: 12ms
memory: 12568kb
input:
136 698
output:
56687290
result:
ok 1 number(s): "56687290"
Test #33:
score: 0
Accepted
time: 20ms
memory: 13780kb
input:
369 401
output:
312325811
result:
ok 1 number(s): "312325811"
Test #34:
score: 0
Accepted
time: 8ms
memory: 11780kb
input:
280 204
output:
280012063
result:
ok 1 number(s): "280012063"
Test #35:
score: 0
Accepted
time: 24ms
memory: 13796kb
input:
904 225
output:
162909174
result:
ok 1 number(s): "162909174"
Test #36:
score: 0
Accepted
time: 92ms
memory: 23024kb
input:
855 928
output:
39885159
result:
ok 1 number(s): "39885159"
Test #37:
score: 0
Accepted
time: 26ms
memory: 13800kb
input:
503 365
output:
745115888
result:
ok 1 number(s): "745115888"
Test #38:
score: 0
Accepted
time: 91ms
memory: 23128kb
input:
646 996
output:
610925577
result:
ok 1 number(s): "610925577"
Test #39:
score: 0
Accepted
time: 103ms
memory: 23124kb
input:
990 918
output:
203469632
result:
ok 1 number(s): "203469632"
Test #40:
score: 0
Accepted
time: 102ms
memory: 23132kb
input:
961 949
output:
169566857
result:
ok 1 number(s): "169566857"
Test #41:
score: 0
Accepted
time: 95ms
memory: 23064kb
input:
946 932
output:
352423195
result:
ok 1 number(s): "352423195"
Test #42:
score: 0
Accepted
time: 98ms
memory: 23040kb
input:
903 981
output:
196309824
result:
ok 1 number(s): "196309824"
Test #43:
score: 0
Accepted
time: 89ms
memory: 23064kb
input:
916 988
output:
487208972
result:
ok 1 number(s): "487208972"
Test #44:
score: 0
Accepted
time: 90ms
memory: 23036kb
input:
982 982
output:
387421488
result:
ok 1 number(s): "387421488"
Test #45:
score: 0
Accepted
time: 96ms
memory: 23052kb
input:
955 911
output:
955637031
result:
ok 1 number(s): "955637031"
Test #46:
score: 0
Accepted
time: 94ms
memory: 23044kb
input:
906 999
output:
798469943
result:
ok 1 number(s): "798469943"
Test #47:
score: 0
Accepted
time: 90ms
memory: 23060kb
input:
982 975
output:
193506289
result:
ok 1 number(s): "193506289"
Test #48:
score: 0
Accepted
time: 88ms
memory: 23068kb
input:
921 991
output:
431202149
result:
ok 1 number(s): "431202149"