結果
| 問題 | No.213 素数サイコロと合成数サイコロ (3-Easy) |
| ユーザー |
 t98slider
|
| 提出日時 | 2022-11-18 02:00:59 |
| 言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 391 ms / 3,000 ms |
| コード長 | 16,809 bytes |
| コンパイル時間 | 1,837 ms |
| コンパイル使用メモリ | 178,236 KB |
| 実行使用メモリ | 6,816 KB |
| 最終ジャッジ日時 | 2024-09-19 12:05:40 |
| 合計ジャッジ時間 | 3,200 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 391 ms
6,816 KB |
| testcase_01 | AC | 353 ms
6,816 KB |
ソースコード
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
namespace internal {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
unsigned int v = (unsigned int)(z % _m);
return v;
}
};
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u;
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
template <class T> using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T> using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
//自分で加えたもの
friend istream& operator>>(istream& os,mint& rhs) noexcept {
long long v;
rhs = mint{(os >> v, v)};
return os;
}
friend constexpr ostream& operator << (ostream &os, const mint& rhs) noexcept {
return os << rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
//自分で加えたもの
friend istream& operator>>(istream& os,mint& rhs) noexcept {
long long v;
rhs = mint{(os >> v, v)};
return os;
}
friend constexpr ostream& operator << (ostream &os, const mint& rhs) noexcept {
return os << rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
using mint = modint1000000007;
using mint2 = modint998244353;
template <class T, size_t N> struct Matrix {
std::array<std::array<T, N>, N> A{};
Matrix() {}
Matrix(const std::array<std::array<T, N>, N> &M) : A(M){}
Matrix(const std::vector<std::vector<T>> &M) {
for(size_t i = 0; i < N; i++){
for(size_t j = 0; j < N; j++){
A[i][j] = M[i][j];
}
}
}
const std::array<T, N>& operator[](int i) const { return A[i]; }
std::array<T, N>& operator[](int i) { return A[i]; }
Matrix& operator+=(const Matrix& rhs) {
for(size_t i = 0; i < N; i++){
for(size_t j = 0; j < N; j++){
A[i][j] += rhs[i][j];
}
}
return *this;
}
Matrix& operator-=(const Matrix& rhs) {
for(size_t i = 0; i < N; i++){
for(size_t j = 0; j < N; j++){
A[i][j] -= rhs[i][j];
}
}
return *this;
}
Matrix& operator*=(const Matrix& rhs) {
std::array<std::array<T, N>, N> res{};
for(size_t i = 0; i < N; i++){
for(size_t j = 0; j < N; j++){
for(size_t k = 0; k < N; k++){
res[i][j] += A[i][k] * rhs[k][j];
}
}
}
swap(A, res);
return *this;
}
Matrix& operator+() const { return *this; }
Matrix& operator-() const { return Matrix() - *this; }
friend Matrix operator+(const Matrix& lhs, const Matrix& rhs) {
return Matrix(lhs) += rhs;
}
friend Matrix operator-(const Matrix& lhs, const Matrix& rhs) {
return Matrix(lhs) -= rhs;
}
friend Matrix operator*(const Matrix& lhs, const Matrix& rhs) {
return Matrix(lhs) *= rhs;
}
friend bool operator==(const Matrix& lhs, const Matrix& rhs) {
return (lhs.A == rhs.A);
}
friend bool operator!=(const Matrix& lhs, const Matrix& rhs) {
return (lhs.A != rhs.A);
}
Matrix pow(long long v){
Matrix res, temp = A;
for(size_t i = 0; i < N; i++)res[i][i] = 1;
while(v){
if(v & 1)res *= temp;
temp *= temp;
v >>= 1;
}
return res;
}
friend std::ostream& operator << (std::ostream &os, const Matrix& rhs) noexcept {
for(size_t i = 0; i < N; i++){
if(i) os << '\n';
for(size_t j = 0; j < N; j++){
os << (j ? " " : "") << rhs[i][j];
}
}
return os;
}
};
/*int main(){
ios::sync_with_stdio(false);
cin.tie(0);
ll N, P, C;
cin >> N >> P >> C;
vector<int> D1 = {2, 3, 5, 7, 11, 13}, D2 = {4, 6, 8, 9, 10, 12};
vector<mint> dp(131);
dp[0] = 1;
while(P--){
vector<mint> ndp(131);
for(int i = 117; i >= 0; i--){
for(int j = 0; j < D1.size(); j++){
ndp[i + D1[j]] += dp[i];
}
}
swap(ndp, dp);
}
while(C--){
vector<mint> ndp(131);
for(int i = 117; i >= 0; i--){
for(int j = 0; j < D2.size(); j++){
ndp[i + D2[j]] += dp[i];
}
}
swap(ndp, dp);
}
Matrix<mint, 131> Mt;
for(int i = 1; i <= 130; i++){
Mt[i - 1][0] = dp[i];
Mt[i - 1][i] = 1;
}
ll e = max(0ll, N - 130);
auto A = Mt.pow(e);
vector<mint> dp2(min(N, 130ll) + 1);
for(int i = 0; i <= 130; i++){
dp2[0] += A[0][i];
}
for(int i = 0; i + 1 < dp2.size(); i++){
for(int j = 1; j < dp.size(); j++){
dp2[min(i + j, int(dp2.size()) - 1)] += dp2[i] * dp[j];
}
}
cout << dp2.back() << '\n';
}*/
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
ll N, P, C;
cin >> N >> P >> C;
vector<int> D1 = {2, 3, 5, 7, 11, 13}, D2 = {4, 6, 8, 9, 10, 12};
vector<mint> dp1(66), dp2(61), dp(131);
function<void(int,int,int)> dfs1 = [&](int i, int s, int v){
if(i == P){dp1[v]++; return; }
for(int j = s; j < 6; j++)dfs1(i + 1, j, v + D1[j]);
};
function<void(int,int,int)> dfs2 = [&](int i, int s, int v){
if(i == C){dp2[v]++; return; }
for(int j = s; j < 6; j++)dfs2(i + 1, j, v + D2[j]);
};
dfs1(0, 0, 0), dfs2(0, 0, 0);
for(int i = 0; i < 66; i++){
for(int j = 0; j < 61; j++){
dp[i + j] += dp1[i] * dp2[j];
}
}
Matrix<mint, 131> Mt;
for(int i = 1; i <= 130; i++){
Mt[i - 1][0] = dp[i];
Mt[i - 1][i] = 1;
}
auto A = Mt.pow(N);
int r = min(N, 130ll);
vector<mint> dp3(r + 1);
for(int i = 0; i <= r; i++){
dp3.rbegin()[i] = A[0][i];
}
mint ans = dp3.back();
for(int i = r - 1; i >= 0; i--){
for(int j = r + 1 - i; j < dp.size(); j++){
ans += dp3[i] * dp[j];
}
}
cout << ans << '\n';
}