結果
| 問題 | No.2249 GCDistance |
| ユーザー |
 KowerKoint2010
|
| 提出日時 | 2023-03-17 22:18:49 |
| 言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 4,179 ms / 5,000 ms |
| コード長 | 26,299 bytes |
| コンパイル時間 | 2,319 ms |
| コンパイル使用メモリ | 219,636 KB |
| 実行使用メモリ | 128,168 KB |
| 最終ジャッジ日時 | 2024-09-18 11:26:29 |
| 合計ジャッジ時間 | 53,557 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 10 |
ソースコード
#line 2 "library/KowerKoint/stl-expansion.hpp"
#include <bits/stdc++.h>
template <typename T1, typename T2>
std::istream& operator>>(std::istream& is, std::pair<T1, T2>& p) {
is >> p.first >> p.second;
return is;
}
template <typename T, size_t N>
std::istream& operator>>(std::istream& is, std::array<T, N>& a) {
for (size_t i = 0; i < N; ++i) {
is >> a[i];
}
return is;
}
template <typename T>
std::istream& operator>>(std::istream& is, std::vector<T>& v) {
for (auto& e : v) is >> e;
return is;
}
template <typename T1, typename T2>
std::ostream& operator<<(std::ostream& os, const std::pair<T1, T2>& p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, size_t N>
std::ostream& operator<<(std::ostream& os, const std::array<T, N>& a) {
for (size_t i = 0; i < N; ++i) {
os << a[i] << (i + 1 == a.size() ? "" : " ");
}
return os;
}
template <typename T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) {
for (size_t i = 0; i < v.size(); ++i) {
os << v[i] << (i + 1 == v.size() ? "" : " ");
}
return os;
}
#line 3 "library/KowerKoint/base.hpp"
using namespace std;
#define REP(i, n) for(int i = 0; i < (int)(n); i++)
#define FOR(i, a, b) for(ll i = a; i < (ll)(b); i++)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define END(...) { print(__VA_ARGS__); return; }
using VI = vector<int>;
using VVI = vector<VI>;
using VVVI = vector<VVI>;
using ll = long long;
using VL = vector<ll>;
using VVL = vector<VL>;
using VVVL = vector<VVL>;
using ull = unsigned long long;
using VUL = vector<ull>;
using VVUL = vector<VUL>;
using VVVUL = vector<VVUL>;
using VD = vector<double>;
using VVD = vector<VD>;
using VVVD = vector<VVD>;
using VS = vector<string>;
using VVS = vector<VS>;
using VVVS = vector<VVS>;
using VC = vector<char>;
using VVC = vector<VC>;
using VVVC = vector<VVC>;
using P = pair<int, int>;
using VP = vector<P>;
using VVP = vector<VP>;
using VVVP = vector<VVP>;
using LP = pair<ll, ll>;
using VLP = vector<LP>;
using VVLP = vector<VLP>;
using VVVLP = vector<VVLP>;
template <typename T>
using PQ = priority_queue<T>;
template <typename T>
using GPQ = priority_queue<T, vector<T>, greater<T>>;
constexpr int INF = 1001001001;
constexpr ll LINF = 1001001001001001001ll;
constexpr int DX[] = {1, 0, -1, 0};
constexpr int DY[] = {0, 1, 0, -1};
void print() { cout << '\n'; }
template<typename T>
void print(const T &t) { cout << t << '\n'; }
template<typename Head, typename... Tail>
void print(const Head &head, const Tail &... tail) {
cout << head << ' ';
print(tail...);
}
#ifdef DEBUG
void dbg() { cerr << '\n'; }
template<typename T>
void dbg(const T &t) { cerr << t << '\n'; }
template<typename Head, typename... Tail>
void dbg(const Head &head, const Tail &... tail) {
cerr << head << ' ';
dbg(tail...);
}
#else
template<typename... Args>
void dbg(const Args &... args) {}
#endif
template<typename T>
vector<vector<T>> split(typename vector<T>::const_iterator begin, typename vector<T>::const_iterator end, T val) {
vector<vector<T>> res;
vector<T> cur;
for(auto it = begin; it != end; it++) {
if(*it == val) {
res.push_back(cur);
cur.clear();
} else cur.push_back(*it);
}
res.push_back(cur);
return res;
}
vector<string> split(typename string::const_iterator begin, typename string::const_iterator end, char val) {
vector<string> res;
string cur = "";
for(auto it = begin; it != end; it++) {
if(*it == val) {
res.push_back(cur);
cur.clear();
} else cur.push_back(*it);
}
res.push_back(cur);
return res;
}
template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }
template <typename T>
pair<VI, vector<T>> compress(const vector<T> &a) {
int n = a.size();
vector<T> x;
REP(i, n) x.push_back(a[i]);
sort(ALL(x)); x.erase(unique(ALL(x)), x.end());
VI res(n);
REP(i, n) res[i] = lower_bound(ALL(x), a[i]) - x.begin();
return make_pair(res, x);
}
template <typename It>
auto rle(It begin, It end) {
vector<pair<typename It::value_type, int>> res;
if(begin == end) return res;
auto pre = *begin;
int num = 1;
for(auto it = begin + 1; it != end; it++) {
if(pre != *it) {
res.emplace_back(pre, num);
pre = *it;
num = 1;
} else num++;
}
res.emplace_back(pre, num);
return res;
}
template <typename It>
vector<pair<typename It::value_type, int>> rle_sort(It begin, It end) {
vector<typename It::value_type> cloned(begin, end);
sort(ALL(cloned));
auto e = rle(ALL(cloned));
sort(ALL(e), [](const auto& l, const auto& r) { return l.second < r.second; });
return e;
}
template <typename T>
pair<vector<T>, vector<T>> factorial(int n) {
vector<T> res(n+1), rev(n+1);
res[0] = 1;
REP(i, n) res[i+1] = res[i] * (i+1);
rev[n] = 1 / res[n];
for(int i = n; i > 0; i--) {
rev[i-1] = rev[i] * i;
}
return make_pair(res, rev);
}
#line 3 "library/KowerKoint/integer/extgcd.hpp"
constexpr ll extgcd(ll a, ll b, ll& x, ll& y) {
x = 1, y = 0;
ll nx = 0, ny = 1;
while(b) {
ll q = a / b;
ll r = a % b;
a = b, b = r;
ll nnx = x - q * nx;
ll nny = y - q * ny;
x = nx, nx = nnx;
y = ny, ny = nny;
}
return a;
}
#line 3 "library/KowerKoint/integer/pow-mod.hpp"
constexpr ll inv_mod(ll n, ll m) {
n %= m;
if (n < 0) n += m;
ll x = -1, y = -1;
if(extgcd(n, m, x, y) != 1) throw logic_error("");
x %= m;
if(x < 0) x += m;
return x;
}
constexpr ll pow_mod(ll a, ll n, ll m) {
if(n == 0) return 1LL;
if(n < 0) return inv_mod(pow_mod(a, -n, m), m);
a %= m;
if (a < 0) n += m;
ll res = 1;
while(n) {
if(n & 1) {
res *= a;
res %= m;
}
n >>= 1;
a *= a;
a %= m;
}
return res;
}
#line 3 "library/KowerKoint/algebra/field.hpp"
template <typename T>
struct SumGroupBase {
constexpr static bool defzero = false;
using Coef = nullptr_t;
using Scalar = nullptr_t;
};
template <typename T>
struct ProdGroupBase {
constexpr static bool defone = false;
};
template <typename T>
struct RepresentationBase {
using R = T;
constexpr static T construct(const R& x) { return x; }
constexpr static R represent(const T& x) { return x; }
};
template <typename T>
struct CompareBase {
constexpr static bool eq(const T& x, const T& y) { return x == y; }
constexpr static bool lt(const T& x, const T& y) { return x < y; }
};
template <typename T>
struct FinitePropertyBase {
constexpr static bool is_finite = false;
};
template <typename T, typename SumGroup = SumGroupBase<T>, typename ProdGroup = ProdGroupBase<T>, typename Representation = RepresentationBase<T>, typename Compare = CompareBase<T>, typename FiniteProperty = FinitePropertyBase<T>>
struct Field {
using R = typename Representation::R;
using Coef = typename SumGroup::Coef;
using Scalar = typename SumGroup::Scalar;
T val;
constexpr static Field zero() {
return SumGroup::zero;
}
constexpr static Field one() {
return ProdGroup::one;
}
constexpr static bool defzero = SumGroup::defzero;
constexpr static bool defone = ProdGroup::defone;
constexpr static bool is_finite = FiniteProperty::is_finite;
constexpr Field() {
if constexpr(SumGroup::defzero) val = SumGroup::zero;
else if constexpr(SumGroup::defone) val = ProdGroup::one;
else val = T();
}
constexpr Field(const R& r) : val(Representation::construct(r)) {}
constexpr R represent() const { return Representation::represent(val); }
constexpr decltype(auto) operator[](size_t i) const {
return val[i];
}
constexpr static Field premitive_root() {
return FiniteProperty::premitive_root();
}
constexpr static size_t order() {
return FiniteProperty::order();
}
constexpr Field& operator*=(const Field& other) {
ProdGroup::mulassign(val, other.val);
return *this;
}
constexpr Field operator*(const Field& other) const {
return Field(*this) *= other;
}
constexpr Field inv() const {
return ProdGroup::inv(val);
}
constexpr Field& operator/=(const Field& other) {
return *this *= other.inv();
}
constexpr Field operator/(const Field& other) const {
return Field(*this) /= other;
}
constexpr Field pow(ll n) const {
if(n < 0) {
return inv().pow(-n);
}
Field res = one();
Field a = *this;
while(n > 0) {
if(n & 1) res *= a;
a *= a;
n >>= 1;
}
return res;
}
constexpr Field operator+() const {
return *this;
}
constexpr Field& operator+=(const Field& other) {
SumGroup::addassign(val, other.val);
return *this;
}
constexpr Field operator+(const Field& other) const {
return Field(*this) += other;
}
constexpr Field operator-() const {
return SumGroup::minus(val);
}
constexpr Field& operator-=(const Field& other) {
return *this += -other;
}
constexpr Field operator-(const Field& other) const {
return Field(*this) -= other;
}
constexpr Field& operator++() {
return *this += one();
}
Field operator++(int) {
Field ret = *this;
++*this;
return ret;
}
constexpr Field& operator--() {
return *this -= one();
}
Field operator--(int) {
Field ret = *this;
--*this;
return ret;
}
constexpr Field& operator*=(const Coef& other) {
SumGroup::coefassign(val, other);
return *this;
}
constexpr Field operator*(const Coef& other) const {
return Field(*this) *= other;
}
constexpr Scalar dot(const Field& other) const {
return SumGroup::dot(val, other.val);
}
constexpr Scalar norm() const {
return dot(*this);
}
constexpr bool operator==(const Field& other) const {
return Compare::eq(val, other.val);
}
constexpr bool operator!=(const Field& other) const {
return !(*this == other);
}
constexpr bool operator<(const Field& other) const {
return Compare::lt(represent(), other.represent());
}
constexpr bool operator>(const Field& other) const {
return other < *this;
}
constexpr bool operator<=(const Field& other) const {
return !(*this > other);
}
constexpr bool operator>=(const Field& other) const {
return !(*this < other);
}
friend istream& operator>>(istream& is, Field& f) {
R r; is >> r;
f = r;
return is;
}
friend ostream& operator<<(ostream& os, const Field& f) {
return os << f.represent();
}
};
namespace std {
template <typename T>
struct hash<Field<T>> {
size_t operator()(const Field<T>& f) const {
return hash<typename Field<T>::R>()(f.represent());
}
};
}
template <typename>
struct is_field : false_type {};
template <typename T, typename SumGroup, typename ProdGroup, typename Representation, typename FiniteProperty>
struct is_field<Field<T, SumGroup, ProdGroup, Representation, FiniteProperty>> : true_type {};
template <typename T>
constexpr bool is_field_v = is_field<T>::value;
template <typename T>
constexpr T zero() {
if constexpr(is_field_v<T>) return T::zero();
else return 0;
}
template <typename T>
constexpr T one() {
if constexpr(is_field_v<T>) return T::one();
else return 1;
}
template <typename T>
constexpr bool is_finite() {
if constexpr(is_field_v<T>) return T::is_finite;
else return false;
}
#line 4 "library/KowerKoint/algebra/modint.hpp"
template <ll mod>
struct SumGroupModint : SumGroupBase<ll> {
static ll& addassign(ll& l, const ll& r) {
ll ret;
if(__builtin_add_overflow(l, r, &ret)) {
l = l % mod + r % mod;
} else {
l = ret;
}
return l;
}
constexpr static bool defzero = true;
constexpr static ll zero = 0;
constexpr static ll minus(const ll& x) {
return -x;
}
};
template <ll mod>
struct ProdGroupModint : ProdGroupBase<ll> {
constexpr static bool defmul = true;
static ll& mulassign(ll& l, const ll& r) {
ll ret;
if(__builtin_mul_overflow(l, r, &ret)) {
l = (l % mod) * (r % mod);
} else {
l = ret;
}
return l;
}
constexpr static bool defone = true;
constexpr static ll one = 1;
constexpr static bool definv = true;
constexpr static ll inv(const ll& x) {
return inv_mod(x, mod);
}
};
template <ll mod>
struct RepresentationModint : RepresentationBase<ll> {
using R = ll;
constexpr static ll construct(const R& x) { return x % mod; }
constexpr static R represent(const ll& x) {
ll ret = x % mod;
if(ret < 0) ret += mod;
return ret;
}
};
template <ll mod>
struct CompareModint : CompareBase<ll> {
constexpr static bool lt(const ll& l, const ll& r) {
return RepresentationModint<mod>::represent(l) < RepresentationModint<mod>::represent(r);
}
constexpr static bool eq(const ll& l, const ll& r) {
return RepresentationModint<mod>::represent(l) == RepresentationModint<mod>::represent(r);
}
};
template <ll mod>
struct FinitePropertyModint : FinitePropertyBase<ll> {
constexpr static bool is_finite = true;
constexpr static ll premitive_root() {
static_assert(mod == 998244353);
return 3;
}
constexpr static size_t order() {
return mod - 1;
}
};
template <ll mod>
using Modint = Field<ll, SumGroupModint<mod>, ProdGroupModint<mod>, RepresentationModint<mod>, CompareModint<mod>, FinitePropertyModint<mod>>;
using MI3 = Modint<998244353>;
using V3 = vector<MI3>;
using VV3 = vector<V3>;
using VVV3 = vector<VV3>;
using MI7 = Modint<1000000007>;
using V7 = vector<MI7>;
using VV7 = vector<V7>;
using VVV7 = vector<VV7>;
#line 3 "library/KowerKoint/counting/counting.hpp"
template <typename T>
struct Counting {
vector<T> fact, ifact;
Counting() {}
Counting(ll n) {
assert(n >= 0);
expand(n);
}
void expand(ll n) {
assert(n >= 0);
ll sz = (ll)fact.size();
if(sz > n) return;
fact.resize(n+1);
ifact.resize(n+1);
fact[0] = 1;
FOR(i, max(1LL, sz), n+1) fact[i] = fact[i-1] * i;
ifact[n] = fact[n].inv();
for(ll i = n-1; i >= sz; i--) ifact[i] = ifact[i+1] * (i+1);
}
T p(ll n, ll r) {
if(n < r) return 0;
assert(r >= 0);
expand(n);
return fact[n] * ifact[n-r];
}
T c(ll n, ll r) {
if(n < r) return 0;
assert(r >= 0);
expand(n);
return fact[n] * ifact[r] * ifact[n-r];
}
T h(ll n, ll r) {
assert(n >= 0);
assert(r >= 0);
return c(n+r-1, r);
}
T stirling(ll n, ll k) {
if(n < k) return 0;
assert(k >= 0);
if(n == 0) return 1;
T res = 0;
T sign = k%2? -1 : 1;
expand(k);
REP(i, k+1) {
res += sign * ifact[i] * ifact[k-i] * T(i).pow(n);
sign *= -1;
}
return res;
}
vector<vector<T>> stirling_table(ll n, ll k) {
assert(n >= 0 && k >= 0);
vector<vector<T>> res(n+1, vector<T>(k+1));
res[0][0] = 1;
FOR(i, 1, n+1) FOR(j, 1, k+1) {
res[i][j] = res[i-1][j-1] + j * res[i-1][j];
}
return res;
}
T bell(ll n, ll k) {
assert(n >= 0 && k >= 0);
expand(k);
vector<T> tmp(k+1);
T sign = 1;
tmp[0] = 1;
FOR(i, 1, k+1) {
sign *= -1;
tmp[i] = tmp[i-1] + sign * ifact[i];
}
T res = 0;
REP(i, k+1) {
res += T(i).pow(n) * ifact[i] * tmp[k-i];
}
return res;
}
vector<vector<T>> partition_table(ll n, ll k) {
assert(n >= 0 && k >= 0);
vector<vector<T>> res(n+1, vector<T>(k+1));
REP(i, k+1) res[0][i] = 1;
FOR(i, 1, n+1) FOR(j, 1, k+1) {
res[i][j] = res[i][j-1] + (i<j? 0 : res[i-j][j]);
}
return res;
}
};
#line 3 "library/KowerKoint/integer/kth-root-integer.hpp"
ull kth_root_integer(ull x, ull k) {
if(k == 1) return x;
ll res = 0;
for(int i = 31; i >= 0; i--) {
bool over = false;
ull tmp = 1;
ull nxt = res | 1ULL << i;
REP(i, k) {
if(tmp > x / nxt) {
over = true;
break;
}
tmp *= nxt;
}
if(!over) res = nxt;
}
return res;
}
#line 2 "library/KowerKoint/bit/bitset.hpp"
struct Bitset {
private:
constexpr static ull mask[] = {
0x0000000000000000ull, 0x0000000000000001ull, 0x0000000000000003ull, 0x0000000000000007ull,
0x000000000000000Full, 0x000000000000001Full, 0x000000000000003Full, 0x000000000000007Full,
0x00000000000000FFull, 0x00000000000001FFull, 0x00000000000003FFull, 0x00000000000007FFull,
0x0000000000000FFFull, 0x0000000000001FFFull, 0x0000000000003FFFull, 0x0000000000007FFFull,
0x000000000000FFFFull, 0x000000000001FFFFull, 0x000000000003FFFFull, 0x000000000007FFFFull,
0x00000000000FFFFFull, 0x00000000001FFFFFull, 0x00000000003FFFFFull, 0x00000000007FFFFFull,
0x0000000000FFFFFFull, 0x0000000001FFFFFFull, 0x0000000003FFFFFFull, 0x0000000007FFFFFFull,
0x000000000FFFFFFFull, 0x000000001FFFFFFFull, 0x000000003FFFFFFFull, 0x000000007FFFFFFFull,
0x00000000FFFFFFFFull, 0x00000001FFFFFFFFull, 0x00000003FFFFFFFFull, 0x00000007FFFFFFFFull,
0x0000000FFFFFFFFFull, 0x0000001FFFFFFFFFull, 0x0000003FFFFFFFFFull, 0x0000007FFFFFFFFFull,
0x000000FFFFFFFFFFull, 0x000001FFFFFFFFFFull, 0x000003FFFFFFFFFFull, 0x000007FFFFFFFFFFull,
0x00000FFFFFFFFFFFull, 0x00001FFFFFFFFFFFull, 0x00003FFFFFFFFFFFull, 0x00007FFFFFFFFFFFull,
0x0000FFFFFFFFFFFFull, 0x0001FFFFFFFFFFFFull, 0x0003FFFFFFFFFFFFull, 0x0007FFFFFFFFFFFFull,
0x000FFFFFFFFFFFFFull, 0x001FFFFFFFFFFFFFull, 0x003FFFFFFFFFFFFFull, 0x007FFFFFFFFFFFFFull,
0x00FFFFFFFFFFFFFFull, 0x01FFFFFFFFFFFFFFull, 0x03FFFFFFFFFFFFFFull, 0x07FFFFFFFFFFFFFFull,
0x0FFFFFFFFFFFFFFFull, 0x1FFFFFFFFFFFFFFFull, 0x3FFFFFFFFFFFFFFFull, 0x7FFFFFFFFFFFFFFFull,
0xFFFFFFFFFFFFFFFFull
};
void correct() {
if(n % 64) v[bnum-1] &= mask[n % 64];
}
public:
vector<ull> v;
int n, bnum;
Bitset(int n_ = 0) : n(n_) {
assert(n_ >= 0);
bnum = (n+63) / 64;
v.resize(bnum);
}
int operator[](int i) const {
assert(0 <= i && i < n);
return (v[i/64] >> (i%64)) & 1;
}
int count() const {
int c = 0;
for (int i = 0; i < v.size(); i++) {
c += __builtin_popcountll(v[i]);
}
return c;
}
// not tested
int count_range(int l, int r) const {
assert(0 <= l && l <= r && r <= n);
int c = 0;
int l2 = l / 64;
int r2 = r / 64;
for(int i = l2; i < r2; i++) {
c += __builtin_popcountll(v[i]);
}
if(l % 64) {
c -= __builtin_popcountll(v[l2] & mask[l % 64]);
}
if(r % 64) {
c += __builtin_popcountll(v[r2] & mask[r % 64]);
}
return c;
}
bool all() const {
return count() == n;
}
bool any() const {
return count() > 0;
}
bool none() const {
return count() == 0;
}
void set(int i) {
assert(0 <= i && i < n);
v[i / 64] |= 1ull << (i % 64);
}
void reset(int i) {
assert(0 <= i && i < n);
v[i / 64] &= ~(1ull << (i % 64));
}
void flip(int i) {
assert(0 <= i && i < n);
v[i / 64] ^= 1ull << (i % 64);
}
void resize(int n_) {
assert(n_ >= 0);
n = n_;
bnum = (n+63) / 64;
v.resize(bnum);
correct();
}
void all_set() {
fill(v.begin(), v.end(), ~0ULL);
correct();
}
void all_reset() {
fill(v.begin(), v.end(), 0);
}
void all_flip() {
for (int i = 0; i < v.size(); i++) {
v[i] = ~v[i];
}
correct();
}
Bitset& operator&=(const Bitset& b) {
assert(n == b.n);
for(int i = 0; i < min(bnum, b.bnum); i++) {
v[i] &= b.v[i];
}
return *this;
}
Bitset operator&(const Bitset& b) const {
assert(n == b.n);
return Bitset(*this) &= b;
}
Bitset& operator|=(const Bitset& b) {
assert(n == b.n);
for(int i = 0; i < min(bnum, b.bnum); i++) {
v[i] |= b.v[i];
}
correct();
return *this;
}
Bitset operator|(const Bitset& b) const {
assert(n == b.n);
return Bitset(*this) |= b;
}
Bitset& operator^=(const Bitset& b) {
assert(n == b.n);
for(int i = 0; i < min(bnum, b.bnum); i++) {
v[i] ^= b.v[i];
}
correct();
return *this;
}
Bitset operator^(const Bitset& b) const {
assert(n == b.n);
return Bitset(*this) ^= b;
}
Bitset operator~() const {
Bitset b(*this);
b.all_flip();
return b;
}
bool operator==(const Bitset& b) const {
assert(n == b.n);
return v == b.v;
}
bool operator!=(const Bitset& b) const {
assert(n == b.n);
return v != b.v;
}
Bitset& operator<<=(int sz) {
assert(sz >= 0);
for(int i = bnum-1; i >= 0; i--) {
if(i-sz/64 < 0) v[i] = 0;
else if(i-sz/64-1 < 0 || sz%64 == 0) v[i] = v[i-sz/64] << (sz%64);
else v[i] = (v[i-sz/64] << (sz%64)) | (v[i-sz/64-1] >> (64-sz%64));
}
correct();
return *this;
}
Bitset operator<<(int sz) const {
assert(sz >= 0);
return Bitset(*this) <<= sz;
}
Bitset& operator>>=(int sz) {
assert(sz >= 0);
for(int i = 0; i < bnum; i++) {
if(i+sz/64 < bnum) v[i] = v[i+sz/64] >> (sz%64);
if(i+sz/64+1 < bnum) v[i] |= v[i+sz/64+1] << (64-sz%64);
}
return *this;
}
Bitset operator>>(int sz) const {
assert(sz >= 0);
return Bitset(*this) >>= sz;
}
};
#line 4 "library/KowerKoint/integer/prime.hpp"
struct Prime {
Bitset sieved;
VI primes;
Prime() {}
Prime(int n) {
assert(n >= 0);
expand(n);
}
void expand(int n) {
assert(n >= 0);
int sz = (int)sieved.n - 1;
if(n <= sz) return;
sieved.resize(n+1);
sieved.set(0);
sieved.set(1);
primes.clear();
if(n >= 2) primes.push_back(2);
for(int d = 3; d <= n; d += 2) {
if(!sieved[d]) {
primes.push_back(d);
for(ll i = (ll)d*d; i <= n; i += d*2) sieved.set(i);
}
}
}
bool is_prime(ull n) {
assert(n > 0);
if(n == 2) return true;
if(!(n & 1)) return false;
if(n+1 <= (ull)sieved.n) return !sieved[n];
for(ull d = 2; d*d <= n; d++) {
if(n % d == 0) return false;
}
return true;
}
VI prime_list(int n) {
assert(n > 0);
expand(n);
return VI(primes.begin(), upper_bound(ALL(primes), n));
}
vector<pair<ull, int>> prime_factor(ull n) {
assert(n > 0);
vector<pair<ull, int>> factor;
expand(kth_root_integer(n, 2));
for(ull prime : primes) {
if(prime * prime > n) break;
int cnt = 0;
while(n % prime == 0) {
n /= prime;
cnt++;
}
if(cnt) factor.emplace_back(prime, cnt);
}
if(n > 1) factor.emplace_back(n, 1);
return factor;
}
VUL divisor(ull n) {
assert(n > 0);
auto factor = prime_factor(n);
VUL res = {1};
for(auto [prime, cnt] : factor) {
int sz = res.size();
res.resize(sz * (cnt+1));
REP(i, sz*cnt) res[sz+i] = res[i] * prime;
REP(i, cnt) inplace_merge(res.begin(), res.begin() + sz*(i+1), res.begin() + sz*(i+2));
}
return res;
}
};
#line 3 "Contests/yukicoder_381/yukicoder_381_d/main.cpp"
/* #include <atcoder/all> */
/* using namespace atcoder; */
/* #include "KowerKoint/expansion/ac-library/all.hpp" */
void solve(){
int max_n = 10000000;
Prime pr(max_n);
VI prime_list = pr.prime_list(max_n);
VI totient(max_n+1);
for(int i =1; i <= max_n; i++) {
totient[i] = i;
int x = i;
for(int j = 0; j < prime_list.size() && prime_list[j] * prime_list[j] <= x; j++) {
if(x % prime_list[j] == 0) {
totient[i] = totient[i] / prime_list[j] * (prime_list[j] - 1);
while(x % prime_list[j] == 0) x /= prime_list[j];
}
}
if(x > 1) totient[i] = totient[i] / x * (x - 1);
}
VL totient_sum(ALL(totient));
REP(i, max_n) totient_sum[i+1] += totient_sum[i];
int t; cin >> t;
while(t--) {
ll n; cin >> n;
print(n*(n-1) - totient_sum[n]+1);
}
}
// generated by oj-template v4.7.2 (https://github.com/online-judge-tools/template-generator)
int main() {
// Fasterize input/output script
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(100);
// scanf/printf user should delete this fasterize input/output script
int t = 1;
//cin >> t; // comment out if solving multi testcase
for(int testCase = 1;testCase <= t;++testCase){
solve();
}
return 0;
}