結果

問題 No.1100 Boxes
ユーザー fastmath
提出日時 2020-06-26 22:46:43
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 107 ms / 2,000 ms
コード長 10,878 bytes
コンパイル時間 2,414 ms
コンパイル使用メモリ 192,044 KB
実行使用メモリ 21,856 KB
最終ジャッジ日時 2024-07-04 22:43:59
合計ジャッジ時間 4,942 ms
ジャッジサーバーID
(参考情報)
judge2 / judge5
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 4
other AC * 36
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include<bits/stdc++.h>
using namespace std;
#define int long long
#define ii pair <int, int>
#define app push_back
#define all(a) a.begin(), a.end()
#define bp __builtin_popcountll
#define ll long long
#define mp make_pair
#define f first
#define s second
#define Time (double)clock()/CLOCKS_PER_SEC
namespace FFT {
const int md = 998244353;
namespace faq{
inline void add(int &x, int y) {
x += y;
if (x >= md) {
x -= md;
}
}
inline void sub(int &x, int y) {
x -= y;
if (x < 0) {
x += md;
}
}
inline int mul(int x, int y) {
return (long long) x * y % md;
}
inline int power(int x, int y) {
int res = 1;
for (; y; y >>= 1, x = mul(x, x)) {
if (y & 1) {
res = mul(res, x);
}
}
return res;
}
inline int inv(int a) {
a %= md;
if (a < 0) {
a += md;
}
int b = md, u = 0, v = 1;
while (a) {
int t = b / a;
b -= t * a;
swap(a, b);
u -= t * v;
swap(u, v);
}
if (u < 0) {
u += md;
}
return u;
}
namespace ntt {
int base = 1, root = -1, max_base = -1;
vector<int> rev = {0, 1}, roots = {0, 1};
void init() {
int temp = md - 1;
max_base = 0;
while (temp % 2 == 0) {
temp >>= 1;
++max_base;
}
root = 2;
while (true) {
if (power(root, 1 << max_base) == 1 && power(root, 1 << max_base - 1) != 1) {
break;
}
++root;
}
}
void ensure_base(int nbase) {
if (max_base == -1) {
init();
}
if (nbase <= base) {
return;
}
assert(nbase <= max_base);
rev.resize(1 << nbase);
for (int i = 0; i < 1 << nbase; ++i) {
rev[i] = rev[i >> 1] >> 1 | (i & 1) << nbase - 1;
}
roots.resize(1 << nbase);
while (base < nbase) {
int z = power(root, 1 << max_base - 1 - base);
for (int i = 1 << base - 1; i < 1 << base; ++i) {
roots[i << 1] = roots[i];
roots[i << 1 | 1] = mul(roots[i], z);
}
++base;
}
}
void dft(vector<int> &a) {
int n = a.size(), zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for (int i = 0; i < n; ++i) {
if (i < rev[i] >> shift) {
swap(a[i], a[rev[i] >> shift]);
}
}
for (int i = 1; i < n; i <<= 1) {
for (int j = 0; j < n; j += i << 1) {
for (int k = 0; k < i; ++k) {
int x = a[j + k], y = mul(a[j + k + i], roots[i + k]);
a[j + k] = (x + y) % md;
a[j + k + i] = (x + md - y) % md;
}
}
}
}
vector<int> multiply(vector<int> a, vector<int> b) {
int need = a.size() + b.size() - 1, nbase = 0;
while (1 << nbase < need) {
++nbase;
}
ensure_base(nbase);
int sz = 1 << nbase;
a.resize(sz);
b.resize(sz);
bool equal = a == b;
dft(a);
if (equal) {
b = a;
} else {
dft(b);
}
int inv_sz = inv(sz);
for (int i = 0; i < sz; ++i) {
a[i] = mul(mul(a[i], b[i]), inv_sz);
}
reverse(a.begin() + 1, a.end());
dft(a);
a.resize(need);
return a;
}
vector<int> inverse(vector<int> a) {
int n = a.size(), m = n + 1 >> 1;
if (n == 1) {
return vector<int>(1, inv(a[0]));
} else {
vector<int> b = inverse(vector<int>(a.begin(), a.begin() + m));
int need = n << 1, nbase = 0;
while (1 << nbase < need) {
++nbase;
}
ensure_base(nbase);
int sz = 1 << nbase;
a.resize(sz);
b.resize(sz);
dft(a);
dft(b);
int inv_sz = inv(sz);
for (int i = 0; i < sz; ++i) {
a[i] = mul(mul(md + 2 - mul(a[i], b[i]), b[i]), inv_sz);
}
reverse(a.begin() + 1, a.end());
dft(a);
a.resize(n);
return a;
}
}
}
using ntt::multiply;
using ntt::inverse;
vector<int>& operator += (vector<int> &a, const vector<int> &b) {
if (a.size() < b.size()) {
a.resize(b.size());
}
for (int i = 0; i < b.size(); ++i) {
add(a[i], b[i]);
}
return a;
}
vector<int> operator + (const vector<int> &a, const vector<int> &b) {
vector<int> c = a;
return c += b;
}
vector<int>& operator -= (vector<int> &a, const vector<int> &b) {
if (a.size() < b.size()) {
a.resize(b.size());
}
for (int i = 0; i < b.size(); ++i) {
sub(a[i], b[i]);
}
return a;
}
vector<int> operator - (const vector<int> &a, const vector<int> &b) {
vector<int> c = a;
return c -= b;
}
vector<int>& operator *= (vector<int> &a, const vector<int> &b) {
if (min(a.size(), b.size()) < 128) {
vector<int> c = a;
a.assign(a.size() + b.size() - 1, 0);
for (int i = 0; i < c.size(); ++i) {
for (int j = 0; j < b.size(); ++j) {
add(a[i + j], mul(c[i], b[j]));
}
}
} else {
a = multiply(a, b);
}
return a;
}
vector<int> operator * (const vector<int> &a, const vector<int> &b) {
vector<int> c = a;
return c *= b;
}
vector<int>& operator /= (vector<int> &a, const vector<int> &b) {
int n = a.size(), m = b.size();
if (n < m) {
a.clear();
} else {
vector<int> c = b;
reverse(a.begin(), a.end());
reverse(c.begin(), c.end());
c.resize(n - m + 1);
a *= inverse(c);
a.erase(a.begin() + n - m + 1, a.end());
reverse(a.begin(), a.end());
}
return a;
}
vector<int> operator / (const vector<int> &a, const vector<int> &b) {
vector<int> c = a;
return c /= b;
}
vector<int>& operator %= (vector<int> &a, const vector<int> &b) {
int n = a.size(), m = b.size();
if (n >= m) {
vector<int> c = (a / b) * b;
a.resize(m - 1);
for (int i = 0; i < m - 1; ++i) {
sub(a[i], c[i]);
}
}
return a;
}
vector<int> operator % (const vector<int> &a, const vector<int> &b) {
vector<int> c = a;
return c %= b;
}
vector<int> derivative(const vector<int> &a) {
int n = a.size();
vector<int> b(n - 1);
for (int i = 1; i < n; ++i) {
b[i - 1] = mul(a[i], i);
}
return b;
}
vector<int> primitive(const vector<int> &a) {
int n = a.size();
vector<int> b(n + 1), invs(n + 1);
for (int i = 1; i <= n; ++i) {
invs[i] = i == 1 ? 1 : mul(md - md / i, invs[md % i]);
b[i] = mul(a[i - 1], invs[i]);
}
return b;
}
vector<int> logarithm(const vector<int> &a) {
vector<int> b = primitive(derivative(a) * inverse(a));
b.resize(a.size());
return b;
}
vector<int> exponent(const vector<int> &a) {
vector<int> b(1, 1);
while (b.size() < a.size()) {
vector<int> c(a.begin(), a.begin() + min(a.size(), b.size() << 1));
add(c[0], 1);
vector<int> old_b = b;
b.resize(b.size() << 1);
c -= logarithm(b);
c *= old_b;
for (int i = b.size() >> 1; i < b.size(); ++i) {
b[i] = c[i];
}
}
b.resize(a.size());
return b;
}
vector<int> power(const vector<int> &a, int m) {
int n = a.size(), p = -1;
vector<int> b(n);
for (int i = 0; i < n; ++i) {
if (a[i]) {
p = i;
break;
}
}
if (p == -1) {
b[0] = !m;
return b;
}
if ((long long) m * p >= n) {
return b;
}
int mu = power(a[p], m), di = inv(a[p]);
vector<int> c(n - m * p);
for (int i = 0; i < n - m * p; ++i) {
c[i] = mul(a[i + p], di);
}
c = logarithm(c);
for (int i = 0; i < n - m * p; ++i) {
c[i] = mul(c[i], m);
}
c = exponent(c);
for (int i = 0; i < n - m * p; ++i) {
b[i + m * p] = mul(c[i], mu);
}
return b;
}
vector<int> sqrt(const vector<int> &a) {
vector<int> b(1, 1);
while (b.size() < a.size()) {
vector<int> c(a.begin(), a.begin() + min(a.size(), b.size() << 1));
vector<int> old_b = b;
b.resize(b.size() << 1);
c *= inverse(b);
for (int i = b.size() >> 1; i < b.size(); ++i) {
b[i] = mul(c[i], md + 1 >> 1);
}
}
b.resize(a.size());
return b;
}
vector<int> multiply_all(int l, int r, vector<vector<int>> &all) {
if (l > r) {
return vector<int>();
} else if (l == r) {
return all[l];
} else {
int y = l + r >> 1;
return multiply_all(l, y, all) * multiply_all(y + 1, r, all);
}
}
vector<int> evaluate(const vector<int> &f, const vector<int> &x) {
int n = x.size();
if (!n) {
return vector<int>();
}
vector<vector<int>> up(n * 2);
for (int i = 0; i < n; ++i) {
up[i + n] = vector<int>{(md - x[i]) % md, 1};
}
for (int i = n - 1; i; --i) {
up[i] = up[i << 1] * up[i << 1 | 1];
}
vector<vector<int>> down(n * 2);
down[1] = f % up[1];
for (int i = 2; i < n * 2; ++i) {
down[i] = down[i >> 1] % up[i];
}
vector<int> y(n);
for (int i = 0; i < n; ++i) {
y[i] = down[i + n][0];
}
return y;
}
vector<int> interpolate(const vector<int> &x, const vector<int> &y) {
int n = x.size();
vector<vector<int>> up(n * 2);
for (int i = 0; i < n; ++i) {
up[i + n] = vector<int>{(md - x[i]) % md, 1};
}
for (int i = n - 1; i; --i) {
up[i] = up[i << 1] * up[i << 1 | 1];
}
vector<int> a = evaluate(derivative(up[1]), x);
for (int i = 0; i < n; ++i) {
a[i] = mul(y[i], inv(a[i]));
}
vector<vector<int>> down(n * 2);
for (int i = 0; i < n; ++i) {
down[i + n] = vector<int>(1, a[i]);
}
for (int i = n - 1; i; --i) {
down[i] = down[i << 1] * up[i << 1 | 1] + down[i << 1 | 1] * up[i << 1];
}
return down[1];
}
}
};
const int MOD = 998244353;
int mod(int n) {
n %= MOD;
if (n < 0) return n + MOD;
else return n;
}
int fp(int a, int p) {
int ans = 1, c = a;
for (int i = 0; (1ll << i) <= p; ++i) {
if ((p >> i) & 1) ans = mod(ans * c);
c = mod(c * c);
}
return ans;
}
int dv(int a, int b) { return mod(a * fp(b, MOD - 2)); }
void add(int &a, int b) {
a = mod(a+b);
}
const int N = 2e5+7;
int f[N], inv[N];
void prec() {
f[0] = 1;
for (int i = 1; i < N; ++i)
f[i] = mod(f[i - 1] * i);
inv[N - 1] = fp(f[N - 1], MOD - 2);
for (int i = N - 2; i >= 0; --i)
inv[i] = mod(inv[i + 1] * (i + 1));
}
int C(int n, int k) {
return mod(f[n] * mod(inv[k] * inv[n - k]));
}
int dp[N]; //n balls to exactly k different boxes
int t[2][N];
signed main() {
#ifdef HOME
freopen("input.txt", "r", stdin);
#else
#define endl '\n'
ios_base::sync_with_stdio(0); cin.tie(0);
#endif
prec();
int n, k;
cin >> n >> k;
/*
for (int i = 0; i <= k; ++i)
for (int j = 0; j <= k; ++j)
add(t[i&1][i+j], inv[i]*inv[j]);
*/
for (int r = 0; r < 2; ++r) {
vector <int> a(k+1);
for (int i = 0; i <= k; ++i) {
a[i] = inv[i];
if (i % 2 != r)
a[i] = 0;
}
vector <int> b(k+1);
for (int i = 0; i <= k; ++i)
b[i] = inv[i];
auto res = FFT::faq::ntt::multiply(a, b);
for (int i = 0; i <= k; ++i)
t[r][i] = res[i];
}
int ans = 0;
int r = (k&1)^1;
for (int i = 1; i <= k; ++i) {
int d = 0;
d = t[r^(i&1)][k-i];
int x = mod(fp(i, n) * C(k, i));
x = mod(x * f[k-i]);
d = mod(d*x);
if ((i&1)^r) {
add(ans, -d);
}
else {
add(ans, d);
}
}
cout << ans << endl;
}
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