結果
問題 | No.2396 等差二項展開 |
ユーザー |
|
提出日時 | 2023-07-28 23:05:05 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,746 ms / 6,000 ms |
コード長 | 14,338 bytes |
コンパイル時間 | 2,245 ms |
コンパイル使用メモリ | 206,492 KB |
最終ジャッジ日時 | 2025-02-15 20:41:50 |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
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ファイルパターン | 結果 |
---|---|
other | AC * 31 |
ソースコード
#include <bits/stdc++.h>using namespace std;#define rep(i, n) for (int i = 0; i < (n); i++)#define per(i, n) for (int i = (n)-1; i >= 0; i--)#define rep2(i, l, r) for (int i = (l); i < (r); i++)#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)#define each(e, v) for (auto &e : v)#define MM << " " <<#define pb push_back#define eb emplace_back#define all(x) begin(x), end(x)#define rall(x) rbegin(x), rend(x)#define sz(x) (int)x.size()using ll = long long;using pii = pair<int, int>;using pil = pair<int, ll>;using pli = pair<ll, int>;using pll = pair<ll, ll>;template <typename T>using minheap = priority_queue<T, vector<T>, greater<T>>;template <typename T>using maxheap = priority_queue<T>;template <typename T>bool chmax(T &x, const T &y) {return (x < y) ? (x = y, true) : false;}template <typename T>bool chmin(T &x, const T &y) {return (x > y) ? (x = y, true) : false;}template <typename T>int flg(T x, int i) {return (x >> i) & 1;}int pct(int x) { return __builtin_popcount(x); }int pct(ll x) { return __builtin_popcountll(x); }int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }template <typename T>void print(const vector<T> &v, T x = 0) {int n = v.size();for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');if (v.empty()) cout << '\n';}template <typename T>void printn(const vector<T> &v, T x = 0) {int n = v.size();for (int i = 0; i < n; i++) cout << v[i] + x << '\n';}template <typename T>int lb(const vector<T> &v, T x) {return lower_bound(begin(v), end(v), x) - begin(v);}template <typename T>int ub(const vector<T> &v, T x) {return upper_bound(begin(v), end(v), x) - begin(v);}template <typename T>void rearrange(vector<T> &v) {sort(begin(v), end(v));v.erase(unique(begin(v), end(v)), end(v));}template <typename T>vector<int> id_sort(const vector<T> &v, bool greater = false) {int n = v.size();vector<int> ret(n);iota(begin(ret), end(ret), 0);sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });return ret;}template <typename T>void reorder(vector<T> &a, const vector<int> &ord) {int n = a.size();vector<T> b(n);for (int i = 0; i < n; i++) b[i] = a[ord[i]];swap(a, b);}template <typename T>T floor(T x, T y) {assert(y != 0);if (y < 0) x = -x, y = -y;return (x >= 0 ? x / y : (x - y + 1) / y);}template <typename T>T ceil(T x, T y) {assert(y != 0);if (y < 0) x = -x, y = -y;return (x >= 0 ? (x + y - 1) / y : x / y);}template <typename S, typename T>pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {return make_pair(p.first + q.first, p.second + q.second);}template <typename S, typename T>pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {return make_pair(p.first - q.first, p.second - q.second);}template <typename S, typename T>istream &operator>>(istream &is, pair<S, T> &p) {S a;T b;is >> a >> b;p = make_pair(a, b);return is;}template <typename S, typename T>ostream &operator<<(ostream &os, const pair<S, T> &p) {return os << p.first << ' ' << p.second;}struct io_setup {io_setup() {ios_base::sync_with_stdio(false);cin.tie(NULL);cout << fixed << setprecision(15);}} io_setup;constexpr int inf = (1 << 30) - 1;constexpr ll INF = (1LL << 60) - 1;// constexpr int MOD = 1000000007;constexpr int MOD = 998244353;struct Runtime_Mod_Int {int x;Runtime_Mod_Int() : x(0) {}Runtime_Mod_Int(long long y) {x = y % get_mod();if (x < 0) x += get_mod();}static inline int &get_mod() {static int mod = 0;return mod;}static void set_mod(int md) { get_mod() = md; }Runtime_Mod_Int &operator+=(const Runtime_Mod_Int &p) {if ((x += p.x) >= get_mod()) x -= get_mod();return *this;}Runtime_Mod_Int &operator-=(const Runtime_Mod_Int &p) {if ((x += get_mod() - p.x) >= get_mod()) x -= get_mod();return *this;}Runtime_Mod_Int &operator*=(const Runtime_Mod_Int &p) {x = (int)(1LL * x * p.x % get_mod());return *this;}Runtime_Mod_Int &operator/=(const Runtime_Mod_Int &p) {*this *= p.inverse();return *this;}Runtime_Mod_Int &operator++() { return *this += Runtime_Mod_Int(1); }Runtime_Mod_Int operator++(int) {Runtime_Mod_Int tmp = *this;++*this;return tmp;}Runtime_Mod_Int &operator--() { return *this -= Runtime_Mod_Int(1); }Runtime_Mod_Int operator--(int) {Runtime_Mod_Int tmp = *this;--*this;return tmp;}Runtime_Mod_Int operator-() const { return Runtime_Mod_Int(-x); }Runtime_Mod_Int operator+(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) += p; }Runtime_Mod_Int operator-(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) -= p; }Runtime_Mod_Int operator*(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) *= p; }Runtime_Mod_Int operator/(const Runtime_Mod_Int &p) const { return Runtime_Mod_Int(*this) /= p; }bool operator==(const Runtime_Mod_Int &p) const { return x == p.x; }bool operator!=(const Runtime_Mod_Int &p) const { return x != p.x; }Runtime_Mod_Int inverse() const {assert(*this != Runtime_Mod_Int(0));return pow(get_mod() - 2);}Runtime_Mod_Int pow(long long k) const {Runtime_Mod_Int now = *this, ret = 1;for (; k > 0; k >>= 1, now *= now) {if (k & 1) ret *= now;}return ret;}friend ostream &operator<<(ostream &os, const Runtime_Mod_Int &p) { return os << p.x; }friend istream &operator>>(istream &is, Runtime_Mod_Int &p) {long long a;is >> a;p = Runtime_Mod_Int(a);return is;}};using mint = Runtime_Mod_Int;template <typename T>struct Matrix {vector<vector<T>> A;int n, m;Matrix(int n, int m) : A(n, vector<T>(m, 0)), n(n), m(m) {}inline const vector<T> &operator[](int k) const { return A[k]; }inline vector<T> &operator[](int k) { return A[k]; }static Matrix I(int l) {Matrix ret(l, l);for (int i = 0; i < l; i++) ret[i][i] = 1;return ret;}Matrix &operator*=(const Matrix &B) {assert(m == B.n);Matrix ret(n, B.m);for (int i = 0; i < n; i++) {for (int k = 0; k < m; k++) {for (int j = 0; j < B.m; j++) ret[i][j] += A[i][k] * B[k][j];}}swap(A, ret.A);m = B.m;return *this;}Matrix operator*(const Matrix &B) const { return Matrix(*this) *= B; }Matrix pow(long long k) const {assert(n == m);Matrix now = *this, ret = I(n);for (; k > 0; k >>= 1, now *= now) {if (k & 1) ret *= now;}return ret;}bool eq(const T &a, const T &b) const {return a == b;// return abs(a-b) <= EPS;}// 行基本変形を用いて簡約化を行い、(rank, det) の組を返すpair<int, T> row_reduction(vector<T> &b) {assert((int)b.size() == n);if (n == 0) return make_pair(0, m > 0 ? 0 : 1);int check = 0, rank = 0;T det = (n == m ? 1 : 0);for (int j = 0; j < m; j++) {int pivot = check;for (int i = check; i < n; i++) {if (A[i][j] != 0) pivot = i;// if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T が小数の場合はこちら}if (check != pivot) det *= T(-1);swap(A[check], A[pivot]), swap(b[check], b[pivot]);if (eq(A[check][j], T(0))) {det = T(0);continue;}rank++;det *= A[check][j];T r = T(1) / A[check][j];for (int k = j + 1; k < m; k++) A[check][k] *= r;b[check] *= r;A[check][j] = T(1);for (int i = 0; i < n; i++) {if (i == check) continue;if (!eq(A[i][j], 0)) {for (int k = j + 1; k < m; k++) A[i][k] -= A[i][j] * A[check][k];b[i] -= A[i][j] * b[check];}A[i][j] = T(0);}if (++check == n) break;}return make_pair(rank, det);}pair<int, T> row_reduction() {vector<T> b(n, T(0));return row_reduction(b);}// 行基本変形を行い、逆行列を求めるpair<bool, Matrix> inverse() {if (n != m) return make_pair(false, Matrix(0, 0));if (n == 0) return make_pair(true, Matrix(0, 0));Matrix ret = I(n);for (int j = 0; j < n; j++) {int pivot = j;for (int i = j; i < n; i++) {if (A[i][j] != 0) pivot = i;// if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T が小数の場合はこちら}swap(A[j], A[pivot]), swap(ret[j], ret[pivot]);if (eq(A[j][j], T(0))) return make_pair(false, Matrix(0, 0));T r = T(1) / A[j][j];for (int k = j + 1; k < n; k++) A[j][k] *= r;for (int k = 0; k < n; k++) ret[j][k] *= r;A[j][j] = T(1);for (int i = 0; i < n; i++) {if (i == j) continue;if (!eq(A[i][j], T(0))) {for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[j][k];for (int k = 0; k < n; k++) ret[i][k] -= A[i][j] * ret[j][k];}A[i][j] = T(0);}}return make_pair(true, ret);}// Ax = b の解の 1 つと解空間の基底の組を返すvector<vector<T>> Gaussian_elimination(vector<T> b) {row_reduction(b);vector<vector<T>> ret;vector<int> p(n, m);vector<bool> is_zero(m, true);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) {if (!eq(A[i][j], T(0))) {p[i] = j;break;}}if (p[i] < m) {is_zero[p[i]] = false;} else if (!eq(b[i], T(0))) {return {};}}vector<T> x(m, T(0));for (int i = 0; i < n; i++) {if (p[i] < m) x[p[i]] = b[i];}ret.push_back(x);for (int j = 0; j < m; j++) {if (!is_zero[j]) continue;x[j] = T(1);for (int i = 0; i < n; i++) {if (p[i] < m) x[p[i]] = -A[i][j];}ret.push_back(x);x[j] = T(0);}return ret;}};template <typename T>vector<T> Berlekamp_Massey(const vector<T> &a) {int n = a.size();vector<T> c = {-1}, c_pre = {0};int i_pre = -1;T x_pre = 1;for (int i = 0; i < n; i++) {int d = c.size(), d_pre = c_pre.size();T x = 0;for (int j = 0; j < d; j++) x += a[i - j] * c[j];if (x == 0) continue;T coef = -x / x_pre;if (d >= d_pre + i - i_pre) {for (int j = 0; j < d_pre; j++) c[i - i_pre + j] += coef * c_pre[j];} else {vector<T> memo = c;c.resize(d_pre + i - i_pre);for (int j = 0; j < d_pre; j++) { c[i - i_pre + j] += coef * c_pre[j]; }c_pre = memo, i_pre = i, x_pre = x;}}return c;}template <typename T>struct Kitamasa {// d 項間線形漸化式 a[n] = c[1]*a[n-1]+c[2]*a[n-2]+...+c[d]*a[n-d]const vector<T> a, c;const int d;// f(x) := x^d-c[1]*x^(d-1)-...-c[d-1]*x-c[d]vector<T> f;Kitamasa(const vector<T> &a, const vector<T> &c) : a(a), c(c), d(a.size()) {f.resize(d + 1);f[d] = 1;for (int i = 1; i <= d; i++) f[d - i] = -c[i];}// p(x)*q(x) を f(x) で割った余りvector<T> mul(const vector<T> &p, const vector<T> &q) const {int n = p.size(), m = q.size();vector<T> ret(n + m - 1, 0);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) ret[i + j] += p[i] * q[j];}for (int i = n + m - 2; i >= d; i--) {for (int j = 1; j <= d; j++) ret[i - j] -= ret[i] * f[d - j];}ret.resize(d);return ret;}// p(x)^n を f(x) で割った余りvector<T> pow(vector<T> p, long long n) const {vector<T> ret(1, 0);ret[0] = 1;while (n) {if (n & 1) ret = mul(ret, p);p = mul(p, p), n >>= 1;}return ret;}// a[n] (0-indexed)T operator[](long long n) const {if (n < d) return a[n];vector<T> x(d + 1, 0);x[1] = 1, x = pow(x, n);T ret = 0;for (int i = 0; i < d; i++) ret += x[i] * a[i];return ret;}};void solve() {ll N, M, L, K, B;cin >> N >> M >> L >> K >> B;mint::set_mod(B);auto mul = [&](vector<mint> x) {vector<mint> y(L, 0);y[0] = x[0] + x[L - 1] * mint(M);rep2(i, 1, L) y[i] = x[i - 1] + x[i];return y;};vector comb(L + 1, vector(L + 1, mint(0)));comb[0][0] = 1;rep(i, L) {rep(j, i + 1) {comb[i + 1][j] += comb[i][j];comb[i + 1][j + 1] += comb[i][j];}}vector<mint> a(L);vector<mint> x(L, 0);x[0] = 1;rep(i, L) {a[i] = x[K];x = mul(x);}vector<mint> c(L + 1, 0);rep2(i, 1, L + 1) c[i] = comb[L][i] * (i & 1 ? 1 : -1);c[L] += M;// vector<mint> c = Berlekamp_Massey(a);// print(a), print(c);Kitamasa<mint> lr(a, c);cout << lr[N] << '\n';}int main() {int T = 1;// cin >> T;while (T--) solve();}