結果
| 問題 | No.2181 LRM Question 2 |
| ユーザー |
 tokusakurai
|
| 提出日時 | 2023-01-07 00:13:09 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 210 ms / 2,000 ms |
| コード長 | 17,865 bytes |
| コンパイル時間 | 2,613 ms |
| コンパイル使用メモリ | 221,616 KB |
| 実行使用メモリ | 17,096 KB |
| 最終ジャッジ日時 | 2023-08-20 17:41:46 |
| 合計ジャッジ時間 | 4,521 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge12 |
（要ログイン）
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 | 1 ms
4,380 KB |
| testcase_01 | AC | 1 ms
4,376 KB |
| testcase_02 | AC | 74 ms
4,376 KB |
| testcase_03 | AC | 2 ms
4,376 KB |
| testcase_04 | AC | 2 ms
4,380 KB |
| testcase_05 | AC | 1 ms
4,376 KB |
| testcase_06 | AC | 2 ms
4,380 KB |
| testcase_07 | AC | 1 ms
4,380 KB |
| testcase_08 | AC | 102 ms
4,376 KB |
| testcase_09 | AC | 71 ms
4,380 KB |
| testcase_10 | AC | 109 ms
4,376 KB |
| testcase_11 | AC | 108 ms
4,380 KB |
| testcase_12 | AC | 106 ms
4,380 KB |
| testcase_13 | AC | 2 ms
4,380 KB |
| testcase_14 | AC | 210 ms
17,096 KB |
| testcase_15 | AC | 9 ms
4,376 KB |
| testcase_16 | AC | 168 ms
13,920 KB |
| testcase_17 | AC | 3 ms
4,376 KB |
| testcase_18 | AC | 2 ms
4,376 KB |
| testcase_19 | AC | 4 ms
4,380 KB |
| testcase_20 | AC | 51 ms
6,616 KB |
| testcase_21 | AC | 18 ms
4,380 KB |
| testcase_22 | AC | 4 ms
4,376 KB |
| testcase_23 | AC | 1 ms
4,380 KB |
| testcase_24 | AC | 1 ms
4,376 KB |
| testcase_25 | AC | 1 ms
4,380 KB |
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;
}
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 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;
const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
// const int MOD = 1000000007;
const 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 Combination {
static vector<T> _fac, _ifac;
Combination() {}
static void init(int n) {
_fac.resize(n + 1), _ifac.resize(n + 1);
_fac[0] = 1;
for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i;
_ifac[n] = _fac[n].inverse();
for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i;
}
static T fac(int k) { return _fac[k]; }
static T ifac(int k) { return _ifac[k]; }
static T inv(int k) { return fac(k - 1) * ifac(k); }
static T P(int n, int k) {
if (k < 0 || n < k) return 0;
return fac(n) * ifac(n - k);
}
static T C(int n, int k) {
if (k < 0 || n < k) return 0;
return fac(n) * ifac(n - k) * ifac(k);
}
// k 個の区別できない玉を n 個の区別できる箱に入れる場合の数
static T H(int n, int k) {
if (n < 0 || k < 0) return 0;
return k == 0 ? 1 : C(n + k - 1, k);
}
// n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数
static T second_stirling_number(int n, int k) {
T ret = 0;
for (int i = 0; i <= k; i++) {
T tmp = C(k, i) * T(i).pow(n);
ret += ((k - i) & 1) ? -tmp : tmp;
}
return ret * ifac(k);
}
// n 個の区別できる玉を、k 個の区別しない箱に入れる場合の数
static T bell_number(int n, int k) {
if (n == 0) return 1;
k = min(k, n);
vector<T> pref(k + 1);
pref[0] = 1;
for (int i = 1; i <= k; i++) {
if (i & 1) {
pref[i] = pref[i - 1] - ifac(i);
} else {
pref[i] = pref[i - 1] + ifac(i);
}
}
T ret = 0;
for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i];
return ret;
}
};
template <typename T>
vector<T> Combination<T>::_fac = vector<T>();
template <typename T>
vector<T> Combination<T>::_ifac = vector<T>();
template <typename T>
vector<T> divisors(const T &n) {
vector<T> ret;
for (T i = 1; i * i <= n; i++) {
if (n % i == 0) {
ret.push_back(i);
if (i * i != n) ret.push_back(n / i);
}
}
sort(begin(ret), end(ret));
return ret;
}
template <typename T>
vector<pair<T, int>> prime_factor(T n) {
vector<pair<T, int>> ret;
for (T i = 2; i * i <= n; i++) {
int cnt = 0;
while (n % i == 0) cnt++, n /= i;
if (cnt > 0) ret.emplace_back(i, cnt);
}
if (n > 1) ret.emplace_back(n, 1);
return ret;
}
template <typename T>
bool is_prime(const T &n) {
if (n == 1) return false;
for (T i = 2; i * i <= n; i++) {
if (n % i == 0) return false;
}
return true;
}
// 1,2,...,n のうち k と互いに素である自然数の個数
template <typename T>
T coprime(T n, T k) {
vector<pair<T, int>> ps = prime_factor(k);
int m = ps.size();
T ret = 0;
for (int i = 0; i < (1 << m); i++) {
T prd = 1;
for (int j = 0; j < m; j++) {
if ((i >> j) & 1) prd *= ps[j].first;
}
ret += (__builtin_parity(i) ? -1 : 1) * (n / prd);
}
return ret;
}
vector<bool> Eratosthenes(const int &n) {
vector<bool> ret(n + 1, true);
if (n >= 0) ret[0] = false;
if (n >= 1) ret[1] = false;
for (int i = 2; i * i <= n; i++) {
if (!ret[i]) continue;
for (int j = i + i; j <= n; j += i) ret[j] = false;
}
return ret;
}
vector<int> Eratosthenes2(const int &n) {
vector<int> ret(n + 1);
iota(begin(ret), end(ret), 0);
if (n >= 0) ret[0] = -1;
if (n >= 1) ret[1] = -1;
for (int i = 2; i * i <= n; i++) {
if (ret[i] < i) continue;
for (int j = i + i; j <= n; j += i) ret[j] = min(ret[j], i);
}
return ret;
}
struct Random_Number_Generator {
mt19937_64 mt;
Random_Number_Generator() : mt(chrono::steady_clock::now().time_since_epoch().count()) {}
// [l,r) での一様乱数
int64_t operator()(int64_t l, int64_t r) {
uniform_int_distribution<int64_t> dist(l, r - 1);
return dist(mt);
}
// [0,r) での一様乱数
int64_t operator()(int64_t r) { return (*this)(0, r); }
} rng;
long long modpow(long long x, long long n, const int &m) {
x %= m;
long long ret = 1;
for (; n > 0; n >>= 1, x *= x, x %= m) {
if (n & 1) ret *= x, ret %= m;
}
return ret;
}
template <typename T>
T modinv(T a, const T &m) {
T b = m, u = 1, v = 0;
while (b > 0) {
T t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return u >= 0 ? u % m : (m - (-u) % m) % m;
}
// オイラーの φ 関数 (x と m が互いに素ならば、x^φ(m) ≡ 1 (mod m))
template <typename T>
T Euler_totient(T m) {
T ret = m;
for (T i = 2; i * i <= m; i++) {
if (m % i == 0) ret /= i, ret *= i - 1;
while (m % i == 0) m /= i;
}
if (m > 1) ret /= m, ret *= m - 1;
return ret;
}
// x^k ≡ y (mod m) となる最小の非負整数 k (存在しなければ -1)
int modlog(int x, int y, int m, int max_ans = -1) {
if (max_ans == -1) max_ans = m;
long long g = 1;
for (int i = m; i > 0; i >>= 1) g *= x, g %= m;
g = gcd(g, m);
int c = 0;
long long t = 1;
for (; t % g != 0; c++) {
if (t == y) return c;
t *= x, t %= m;
}
if (y % g != 0) return -1;
t /= g, y /= g, m /= g;
int n = 0;
long long gs = 1;
for (; n * n < max_ans; n++) gs *= x, gs %= m;
unordered_map<int, int> mp;
long long e = y;
for (int i = 0; i < n; mp[e] = ++i) e *= x, e %= m;
e = t;
for (int i = 0; i < n; i++) {
e *= gs, e %= m;
if (mp.count(e)) return c + n * (i + 1) - mp[e];
}
return -1;
}
// x^k ≡ 1 (mod m) となる最小の正整数 k (x と m は互いに素)
template <typename T>
T order(T x, const T &m) {
T n = Euler_totient(m);
vector<T> ds;
for (T i = 1; i * i <= n; i++) {
if (n % i == 0) ds.push_back(i), ds.push_back(n / i);
}
sort(begin(ds), end(ds));
for (auto &e : ds) {
if (modpow(x, e, m) == 1) return e;
}
return -1;
}
// 素数 p の原始根
template <typename T>
T primitive_root(const T &p) {
vector<T> ds;
for (T i = 1; i * i <= p - 1; i++) {
if ((p - 1) % i == 0) ds.push_back(i), ds.push_back((p - 1) / i);
}
sort(begin(ds), end(ds));
while (true) {
T r = rng(1, p);
for (auto &e : ds) {
if (e == p - 1) return r;
if (modpow(r, e, p) == 1) break;
}
}
}
template <typename T>
T _gcd(const T &a, const T &b) {
if (b == 0) return a;
return _gcd(b, a % b);
}
template <typename T>
T _lcm(const T &a, const T &b) {
return a * (b / _gcd(a, b));
}
// |x| と |y| は結果として max(a,b) 以下になる。
template <typename T>
T extgcd(const T &a, const T &b, T &x, T &y) {
if (b == 0) {
x = 1, y = 0;
return a;
}
T g = extgcd(b, a % b, y, x);
y -= (a / b) * x;
return g;
}
int mod(const long long &a, const int &m) {
int ret = a % m;
return ret + (ret < 0 ? m : 0);
}
// a と m は互いに素
int modinv(const int &a, const int &m) {
int x, y;
extgcd(a, m, x, y);
return mod(x, m);
}
// Σ[0<=i<n] floor((ai+b)/m)
template <typename T>
T floor_sum(const T &n, const T &m, T a, T b) {
T ret = (a / m) * (n * (n - 1) / 2) + (b / m) * n;
a %= m, b %= m;
T y = (a * n + b) / m;
if (y == 0) return ret;
ret += floor_sum(y, a, m, a * n - (m * y - b));
return ret;
}
// min{ai+b mod m | 0<=i<n} またがないときコスト p, またぐときコスト q
template <typename T>
T linear_mod_min(T n, const T &m, T a, T b, bool is_min = true, T p = 1, T q = 1) {
if (a == 0) return b;
if (is_min) {
if (b >= a) {
T t = (m - b + a - 1) / a;
T c = (t - 1) * p + q;
if (n <= c) return b;
n -= c;
b += a * t - m;
}
b = a - 1 - b;
} else {
if (b < m - a) {
T t = (m - b - 1) / a;
T c = t * p;
if (n <= c) return a * ((n - 1) / p) + b;
n -= c;
b += a * t;
}
b = m - 1 - b;
}
T d = m / a;
T c = linear_mod_min(n, a, m % a, b, !is_min, (d - 1) * p + q, d * p + q);
return is_min ? a - 1 - c : m - 1 - c;
}
template <typename T>
pair<T, T> Chinese_remainder_theorem(const T &a1, const T &m1, const T &a2, const T &m2) {
T x, y, g = extgcd(m1, m2, x, y);
if ((a2 - a1) % g != 0) return make_pair(0, -1);
T m = m1 * (m2 / g);
T tmp = mod(x * ((a2 - a1) / g), m2 / g);
T a = (m1 * tmp + a1) % m;
return make_pair(a, m);
}
// m の各要素がそれぞれ互いに素とは限らない場合の前処理
bool prepare_Garner(vector<int> &a, vector<int> &m) {
int n = a.size();
for (int i = 0; i < n; i++) {
for (int j = 0; j < i; j++) {
int g = gcd(m[i], m[j]);
if ((a[i] - a[j]) % g != 0) return false;
m[i] /= g, m[j] /= g;
int gi = gcd(m[i], g), gj = g / gi;
do {
g = gcd(gi, gj);
gi *= g, gj /= g;
} while (g > 1);
m[i] *= gi, m[j] *= gj;
}
}
return true;
}
// m の各要素はそれぞれ互いに素
int Garner(vector<int> a, vector<int> m, const int &M) {
m.push_back(M);
vector<long long> coeffs(m.size(), 1);
vector<long long> constants(m.size(), 0);
for (int k = 0; k < (int)a.size(); k++) {
long long x = a[k] - constants[k], y = modinv(coeffs[k], m[k]);
long long t = mod(x * y, m[k]);
for (int i = k + 1; i < (int)m.size(); i++) {
constants[i] += t * coeffs[i], constants[i] %= m[i];
coeffs[i] *= m[k], coeffs[i] %= m[i];
}
}
return constants.back();
}
int main() {
ll L, R, M;
cin >> L >> R >> M;
if (M == 1) {
cout << "0\n";
return 0;
}
auto ps = prime_factor(M);
auto solve = [&](ll l, ll r, ll p, ll c) {
ll q = 1;
rep(i, c) q *= p;
vector<ll> fac(q, 1), ifac(q, 1);
rep2(i, 1, q) {
ll x = i;
while (x % p == 0) x /= p;
if (x != i) x = 1;
fac[i] = fac[i - 1] * x % q;
ifac[i] = modinv(fac[i], q);
}
// print(fac), print(ifac);
auto calc1 = [&](ll n) {
ll cnt = 0;
while (n > 0) {
cnt += n / p;
n /= p;
}
return cnt;
};
auto calc2 = [&](ll n) {
ll ret = 1;
while (n > 0) {
ll t = n / q, m = n % q;
ret *= modpow(fac[q - 1], t, q), ret %= q;
ret *= fac[m], ret %= q;
n /= p;
}
return ret;
};
auto calc3 = [&](ll n) {
ll ret = 1;
while (n > 0) {
ll t = n / q, m = n % q;
ret *= modpow(ifac[q - 1], t, q), ret %= q;
ret *= ifac[m], ret %= q;
n /= p;
}
return ret;
};
ll ret = 0;
ll c1 = calc1(2 * l), m1 = calc2(2 * l);
ll c2 = calc1(l), m2 = calc3(l);
for (ll n = l; n <= r; n++) {
ll t = min(c1 - c2 * 2, c);
ll tmp = (m1 * m2 * m2) % q;
rep(i, t) tmp *= p, tmp %= q;
ret += tmp, ret %= q;
// cout << c1 MM m1 MM c2 MM m2 MM tmp << '\n';
for (ll i = 2 * n + 1; i <= 2 * n + 2; i++) {
ll x = i;
while (x % p == 0) x /= p, c1++;
x %= q;
m1 *= x, m1 %= q;
}
for (ll i = n + 1; i <= n + 1; i++) {
ll x = i;
while (x % p == 0) x /= p, c2++;
x %= q;
m2 *= modinv(x, q), m2 %= q;
}
}
return ret;
};
vector<int> as, ms;
for (auto [p, c] : ps) {
ll q = 1;
rep(i, c) q *= p;
as.eb(solve(L, R, p, c));
ms.eb(q);
}
ll ans = Garner(as, ms, M);
ans += M - ((R - L + 1) * 2) % M;
ans %= M;
cout << ans << '\n';
}