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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#226811 | #6323. Range NEQ | YouKn0wWho | AC ✓ | 490ms | 63804kb | C++23 | 5.0kb | 2023-10-26 16:45:11 | 2023-10-26 16:45:12 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
const int N = 1 << 21;
const int mod = 998244353;
const int root = 3;
int lim, rev[N], w[N], wn[N], inv_lim;
void reduce(int &x) { x = (x + mod) % mod; }
int POW(int x, int y, int ans = 1) {
for (; y; y >>= 1, x = (long long) x * x % mod) if (y & 1) ans = (long long) ans * x % mod;
return ans;
}
void precompute(int len) {
lim = wn[0] = 1; int s = -1;
while (lim < len) lim <<= 1, ++s;
for (int i = 0; i < lim; ++i) rev[i] = rev[i >> 1] >> 1 | (i & 1) << s;
const int g = POW(root, (mod - 1) / lim);
inv_lim = POW(lim, mod - 2);
for (int i = 1; i < lim; ++i) wn[i] = (long long) wn[i - 1] * g % mod;
}
void ntt(vector<int> &a, int typ) {
for (int i = 0; i < lim; ++i) if (i < rev[i]) swap(a[i], a[rev[i]]);
for (int i = 1; i < lim; i <<= 1) {
for (int j = 0, t = lim / i / 2; j < i; ++j) w[j] = wn[j * t];
for (int j = 0; j < lim; j += i << 1) {
for (int k = 0; k < i; ++k) {
const int x = a[k + j], y = (long long) a[k + j + i] * w[k] % mod;
reduce(a[k + j] += y - mod), reduce(a[k + j + i] = x - y);
}
}
}
if (!typ) {
reverse(a.begin() + 1, a.begin() + lim);
for (int i = 0; i < lim; ++i) a[i] = (long long) a[i] * inv_lim % mod;
}
}
vector<int> multiply(vector<int> &f, vector<int> &g) {
int n=(int)f.size() + (int)g.size() - 1;
precompute(n);
vector<int> a = f, b = g;
a.resize(lim); b.resize(lim);
ntt(a, 1), ntt(b, 1);
for (int i = 0; i < lim; ++i) a[i] = (long long) a[i] * b[i] % mod;
ntt(a, 0);
return a;
}
template <const int32_t MOD>
struct modint {
int32_t value;
modint() = default;
modint(int32_t value_) : value(value_) {}
inline modint<MOD> operator + (modint<MOD> other) const { int32_t c = this->value + other.value; return modint<MOD>(c >= MOD ? c - MOD : c); }
inline modint<MOD> operator - (modint<MOD> other) const { int32_t c = this->value - other.value; return modint<MOD>(c < 0 ? c + MOD : c); }
inline modint<MOD> operator * (modint<MOD> other) const { int32_t c = (int64_t)this->value * other.value % MOD; return modint<MOD>(c < 0 ? c + MOD : c); }
inline modint<MOD> & operator += (modint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
inline modint<MOD> & operator -= (modint<MOD> other) { this->value -= other.value; if (this->value < 0) this->value += MOD; return *this; }
inline modint<MOD> & operator *= (modint<MOD> other) { this->value = (int64_t)this->value * other.value % MOD; if (this->value < 0) this->value += MOD; return *this; }
inline modint<MOD> operator - () const { return modint<MOD>(this->value ? MOD - this->value : 0); }
modint<MOD> pow(uint64_t k) const { modint<MOD> x = *this, y = 1; for (; k; k >>= 1) { if (k & 1) y *= x; x *= x; } return y; }
modint<MOD> inv() const { return pow(MOD - 2); } // MOD must be a prime
inline modint<MOD> operator / (modint<MOD> other) const { return *this * other.inv(); }
inline modint<MOD> operator /= (modint<MOD> other) { return *this *= other.inv(); }
inline bool operator == (modint<MOD> other) const { return value == other.value; }
inline bool operator != (modint<MOD> other) const { return value != other.value; }
inline bool operator < (modint<MOD> other) const { return value < other.value; }
inline bool operator > (modint<MOD> other) const { return value > other.value; }
};
template <int32_t MOD> modint<MOD> operator * (int64_t value, modint<MOD> n) { return modint<MOD>(value) * n; }
template <int32_t MOD> modint<MOD> operator * (int32_t value, modint<MOD> n) { return modint<MOD>(value % MOD) * n; }
template <int32_t MOD> istream & operator >> (istream & in, modint<MOD> &n) { return in >> n.value; }
template <int32_t MOD> ostream & operator << (ostream & out, modint<MOD> n) { return out << n.value; }
using mint = modint<mod>;
struct Combi{
int n; vector<mint> facts, finvs, invs;
Combi(int _n): n(_n), facts(_n), finvs(_n), invs(_n){
facts[0] = finvs[0] = 1;
invs[1] = 1;
for (int i = 2; i < n; i++) invs[i] = invs[mod % i] * (-mod / i);
for(int i = 1; i < n; i++){
facts[i] = facts[i - 1] * i;
finvs[i] = finvs[i - 1] * invs[i];
}
}
inline mint fact(int n) { return facts[n]; }
inline mint finv(int n) { return finvs[n]; }
inline mint inv(int n) { return invs[n]; }
inline mint ncr(int n, int k) { return n < k ? 0 : facts[n] * finvs[k] * finvs[n-k]; }
};
Combi C(N);
vector<int> power(vector<int> f, int n) {
auto ans = f;
n--;
while (n) {
if (n & 1) ans = multiply(ans, f);
f = multiply(f, f);
n >>= 1;
}
return ans;
}
int32_t main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int n, m; cin >> n >> m;
vector<int> f(m + 1);
for (int k = 0; k <= m; k++) {
f[k] = (C.ncr(m, k) * C.ncr(m, k) * C.fact(k)).value;
}
auto a = power(f, n);
mint ans = 0;
for (int i = 0; i <= n * m; i++) {
ans += (i & 1 ? mod - 1 : 1) * C.fact(n * m - i) * a[i];
}
cout << ans << '\n';
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 19ms
memory: 31756kb
input:
2 2
output:
4
result:
ok 1 number(s): "4"
Test #2:
score: 0
Accepted
time: 30ms
memory: 31820kb
input:
5 1
output:
44
result:
ok 1 number(s): "44"
Test #3:
score: 0
Accepted
time: 33ms
memory: 38516kb
input:
167 91
output:
284830080
result:
ok 1 number(s): "284830080"
Test #4:
score: 0
Accepted
time: 26ms
memory: 31804kb
input:
2 1
output:
1
result:
ok 1 number(s): "1"
Test #5:
score: 0
Accepted
time: 22ms
memory: 31628kb
input:
2 3
output:
36
result:
ok 1 number(s): "36"
Test #6:
score: 0
Accepted
time: 23ms
memory: 31804kb
input:
2 4
output:
576
result:
ok 1 number(s): "576"
Test #7:
score: 0
Accepted
time: 26ms
memory: 31880kb
input:
3 1
output:
2
result:
ok 1 number(s): "2"
Test #8:
score: 0
Accepted
time: 24ms
memory: 31864kb
input:
3 2
output:
80
result:
ok 1 number(s): "80"
Test #9:
score: 0
Accepted
time: 22ms
memory: 31816kb
input:
3 3
output:
12096
result:
ok 1 number(s): "12096"
Test #10:
score: 0
Accepted
time: 25ms
memory: 31692kb
input:
3 4
output:
4783104
result:
ok 1 number(s): "4783104"
Test #11:
score: 0
Accepted
time: 25ms
memory: 31796kb
input:
4 1
output:
9
result:
ok 1 number(s): "9"
Test #12:
score: 0
Accepted
time: 18ms
memory: 31964kb
input:
4 2
output:
4752
result:
ok 1 number(s): "4752"
Test #13:
score: 0
Accepted
time: 25ms
memory: 31740kb
input:
4 3
output:
17927568
result:
ok 1 number(s): "17927568"
Test #14:
score: 0
Accepted
time: 21ms
memory: 31760kb
input:
4 4
output:
776703752
result:
ok 1 number(s): "776703752"
Test #15:
score: 0
Accepted
time: 23ms
memory: 31692kb
input:
5 2
output:
440192
result:
ok 1 number(s): "440192"
Test #16:
score: 0
Accepted
time: 24ms
memory: 31816kb
input:
5 3
output:
189125068
result:
ok 1 number(s): "189125068"
Test #17:
score: 0
Accepted
time: 23ms
memory: 31688kb
input:
5 4
output:
975434093
result:
ok 1 number(s): "975434093"
Test #18:
score: 0
Accepted
time: 490ms
memory: 63804kb
input:
1000 1000
output:
720037464
result:
ok 1 number(s): "720037464"
Test #19:
score: 0
Accepted
time: 24ms
memory: 32188kb
input:
72 42
output:
638177567
result:
ok 1 number(s): "638177567"
Test #20:
score: 0
Accepted
time: 25ms
memory: 31744kb
input:
15 19
output:
663050288
result:
ok 1 number(s): "663050288"
Test #21:
score: 0
Accepted
time: 26ms
memory: 32272kb
input:
68 89
output:
94365047
result:
ok 1 number(s): "94365047"
Test #22:
score: 0
Accepted
time: 26ms
memory: 32176kb
input:
92 37
output:
652605307
result:
ok 1 number(s): "652605307"
Test #23:
score: 0
Accepted
time: 30ms
memory: 32164kb
input:
61 87
output:
498277867
result:
ok 1 number(s): "498277867"
Test #24:
score: 0
Accepted
time: 21ms
memory: 32184kb
input:
81 40
output:
133095344
result:
ok 1 number(s): "133095344"
Test #25:
score: 0
Accepted
time: 28ms
memory: 31872kb
input:
7 91
output:
524164813
result:
ok 1 number(s): "524164813"
Test #26:
score: 0
Accepted
time: 25ms
memory: 31796kb
input:
31 18
output:
361233485
result:
ok 1 number(s): "361233485"
Test #27:
score: 0
Accepted
time: 28ms
memory: 32136kb
input:
74 54
output:
500686087
result:
ok 1 number(s): "500686087"
Test #28:
score: 0
Accepted
time: 29ms
memory: 31944kb
input:
32 2
output:
586504335
result:
ok 1 number(s): "586504335"
Test #29:
score: 0
Accepted
time: 404ms
memory: 61040kb
input:
656 718
output:
346764298
result:
ok 1 number(s): "346764298"
Test #30:
score: 0
Accepted
time: 122ms
memory: 41672kb
input:
254 689
output:
358078813
result:
ok 1 number(s): "358078813"
Test #31:
score: 0
Accepted
time: 408ms
memory: 61976kb
input:
713 674
output:
914437613
result:
ok 1 number(s): "914437613"
Test #32:
score: 0
Accepted
time: 103ms
memory: 37480kb
input:
136 698
output:
56687290
result:
ok 1 number(s): "56687290"
Test #33:
score: 0
Accepted
time: 119ms
memory: 37348kb
input:
369 401
output:
312325811
result:
ok 1 number(s): "312325811"
Test #34:
score: 0
Accepted
time: 52ms
memory: 34664kb
input:
280 204
output:
280012063
result:
ok 1 number(s): "280012063"
Test #35:
score: 0
Accepted
time: 118ms
memory: 42972kb
input:
904 225
output:
162909174
result:
ok 1 number(s): "162909174"
Test #36:
score: 0
Accepted
time: 449ms
memory: 62128kb
input:
855 928
output:
39885159
result:
ok 1 number(s): "39885159"
Test #37:
score: 0
Accepted
time: 118ms
memory: 41432kb
input:
503 365
output:
745115888
result:
ok 1 number(s): "745115888"
Test #38:
score: 0
Accepted
time: 416ms
memory: 60500kb
input:
646 996
output:
610925577
result:
ok 1 number(s): "610925577"
Test #39:
score: 0
Accepted
time: 475ms
memory: 63044kb
input:
990 918
output:
203469632
result:
ok 1 number(s): "203469632"
Test #40:
score: 0
Accepted
time: 487ms
memory: 63280kb
input:
961 949
output:
169566857
result:
ok 1 number(s): "169566857"
Test #41:
score: 0
Accepted
time: 488ms
memory: 61980kb
input:
946 932
output:
352423195
result:
ok 1 number(s): "352423195"
Test #42:
score: 0
Accepted
time: 460ms
memory: 63400kb
input:
903 981
output:
196309824
result:
ok 1 number(s): "196309824"
Test #43:
score: 0
Accepted
time: 458ms
memory: 63148kb
input:
916 988
output:
487208972
result:
ok 1 number(s): "487208972"
Test #44:
score: 0
Accepted
time: 480ms
memory: 62916kb
input:
982 982
output:
387421488
result:
ok 1 number(s): "387421488"
Test #45:
score: 0
Accepted
time: 486ms
memory: 61932kb
input:
955 911
output:
955637031
result:
ok 1 number(s): "955637031"
Test #46:
score: 0
Accepted
time: 469ms
memory: 61644kb
input:
906 999
output:
798469943
result:
ok 1 number(s): "798469943"
Test #47:
score: 0
Accepted
time: 482ms
memory: 62836kb
input:
982 975
output:
193506289
result:
ok 1 number(s): "193506289"
Test #48:
score: 0
Accepted
time: 460ms
memory: 63068kb
input:
921 991
output:
431202149
result:
ok 1 number(s): "431202149"