結果
| 問題 |
No.2206 Popcount Sum 2
|
| コンテスト | |
| ユーザー |
 NyaanNyaan
|
| 提出日時 | 2023-02-03 23:38:46 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 459 ms / 4,000 ms |
| コード長 | 21,505 bytes |
| コンパイル時間 | 2,694 ms |
| コンパイル使用メモリ | 276,888 KB |
| 最終ジャッジ日時 | 2025-02-10 10:13:13 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 18 |
ソースコード
/**
* date : 2023-02-03 23:38:34
*/
#define NDEBUG
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N,F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(vector<T> &v) {
return next_permutation(begin(v), end(v));
}
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
} // namespace Nyaan
// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
// inout
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
cout << t;
outr(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
// debug
#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif
// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
//
using namespace std;
namespace fastio {
static constexpr int SZ = 1 << 17;
char inbuf[SZ], outbuf[SZ];
int in_left = 0, in_right = 0, out_right = 0;
struct Pre {
char num[40000];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i * 4 + j] = n % 10 + '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
int len = in_right - in_left;
memmove(inbuf, inbuf + in_left, len);
in_right = len + fread(inbuf + len, 1, SZ - len, stdin);
in_left = 0;
}
inline void flush() {
fwrite(outbuf, 1, out_right, stdout);
out_right = 0;
}
inline void skip_space() {
if (in_left + 32 > in_right) load();
while (inbuf[in_left] <= ' ') in_left++;
}
inline void rd(char& c) {
if (in_left + 32 > in_right) load();
c = inbuf[in_left++];
}
template <typename T>
inline void rd(T& x) {
if (in_left + 32 > in_right) load();
char c;
do c = inbuf[in_left++];
while (c < '-');
[[maybe_unused]] bool minus = false;
if constexpr (is_signed<T>::value == true) {
if (c == '-') minus = true, c = inbuf[in_left++];
}
x = 0;
while (c >= '0') {
x = x * 10 + (c & 15);
c = inbuf[in_left++];
}
if constexpr (is_signed<T>::value == true) {
if (minus) x = -x;
}
}
inline void rd() {}
template <typename Head, typename... Tail>
inline void rd(Head& head, Tail&... tail) {
rd(head);
rd(tail...);
}
inline void wt(char c) {
if (out_right > SZ - 32) flush();
outbuf[out_right++] = c;
}
inline void wt(bool b) {
if (out_right > SZ - 32) flush();
outbuf[out_right++] = b ? '1' : '0';
}
inline void wt(const string &s) {
if (out_right + s.size() > SZ - 32) flush();
memcpy(outbuf + out_right, s.data(), sizeof(char) * s.size());
out_right += s.size();
}
template <typename T>
inline void wt(T x) {
if (out_right > SZ - 32) flush();
if (!x) {
outbuf[out_right++] = '0';
return;
}
if constexpr (is_signed<T>::value == true) {
if (x < 0) outbuf[out_right++] = '-', x = -x;
}
int i = 12;
char buf[16];
while (x >= 10000) {
memcpy(buf + i, pre.num + (x % 10000) * 4, 4);
x /= 10000;
i -= 4;
}
if (x < 100) {
if (x < 10) {
outbuf[out_right] = '0' + x;
++out_right;
} else {
uint32_t q = (uint32_t(x) * 205) >> 11;
uint32_t r = uint32_t(x) - q * 10;
outbuf[out_right] = '0' + q;
outbuf[out_right + 1] = '0' + r;
out_right += 2;
}
} else {
if (x < 1000) {
memcpy(outbuf + out_right, pre.num + (x << 2) + 1, 3);
out_right += 3;
} else {
memcpy(outbuf + out_right, pre.num + (x << 2), 4);
out_right += 4;
}
}
memcpy(outbuf + out_right, buf + i + 4, 12 - i);
out_right += 12 - i;
}
inline void wt() {}
template <typename Head, typename... Tail>
inline void wt(Head&& head, Tail&&... tail) {
wt(head);
wt(forward<Tail>(tail)...);
}
template <typename... Args>
inline void wtn(Args&&... x) {
wt(forward<Args>(x)...);
wt('\n');
}
struct Dummy {
Dummy() { atexit(flush); }
} dummy;
} // namespace fastio
using fastio::rd;
using fastio::skip_space;
using fastio::wt;
using fastio::wtn;
//
using namespace std;
struct Fast_Mo {
int N, Q, width;
vector<int> L, R, order;
bool is_build;
Fast_Mo(int _n, int _q) : N(_n), Q(_q), order(Q), is_build(false) {
width = max<int>(1, 1.0 * N / max<double>(1.0, sqrt(Q / 2.0)));
iota(begin(order), end(order), 0);
}
// [l, r)
void insert(int l, int r) {
assert(0 <= l and l <= r and r <= N);
L.push_back(l), R.push_back(r);
}
void build() { sort(), climb(), is_build = true; }
template <typename AL, typename AR, typename DL, typename DR, typename REM>
void run(const AL &add_left, const AR &add_right, const DL &delete_left,
const DR &delete_right, const REM &rem) {
if (!is_build) build();
int nl = 0, nr = 0;
for (auto idx : order) {
while (nl > L[idx]) add_left(--nl);
while (nr < R[idx]) add_right(nr++);
while (nl < L[idx]) delete_left(nl++);
while (nr > R[idx]) delete_right(--nr);
rem(idx);
}
}
private:
void sort() {
assert((int)order.size() == Q);
vector<int> cnt(N + 1), buf(Q);
for (int i = 0; i < Q; i++) cnt[R[i]]++;
for (int i = 1; i < (int)cnt.size(); i++) cnt[i] += cnt[i - 1];
for (int i = 0; i < Q; i++) buf[--cnt[R[i]]] = i;
vector<int> b(Q);
for (int i = 0; i < Q; i++) b[i] = L[i] / width;
cnt.resize(N / width + 1);
fill(begin(cnt), end(cnt), 0);
for (int i = 0; i < Q; i++) cnt[b[i]]++;
for (int i = 1; i < (int)cnt.size(); i++) cnt[i] += cnt[i - 1];
for (int i = 0; i < Q; i++) order[--cnt[b[buf[i]]]] = buf[i];
for (int i = 0, j = 0; i < Q; i = j) {
int bi = b[order[i]];
j = i + 1;
while (j != Q and bi == b[order[j]]) j++;
if (!(bi & 1)) reverse(begin(order) + i, begin(order) + j);
}
}
int dist(int i, int j) { return abs(L[i] - L[j]) + abs(R[i] - R[j]); }
void climb(int iter = 3, int interval = 5) {
vector<int> d(Q - 1);
for (int i = 0; i < Q - 1; i++) d[i] = dist(order[i], order[i + 1]);
while (iter--) {
for (int i = 1; i < Q; i++) {
int pre1 = d[i - 1];
int js = i + 1, je = min<int>(i + interval, Q - 1);
for (int j = je - 1; j >= js; j--) {
int pre2 = d[j];
int now1 = dist(order[i - 1], order[j]);
int now2 = dist(order[i], order[j + 1]);
if (now1 + now2 < pre1 + pre2) {
reverse(begin(order) + i, begin(order) + j + 1);
reverse(begin(d) + i, begin(d) + j);
d[i - 1] = pre1 = now1;
d[j] = now2;
}
}
}
}
}
};
struct Mo {
int width;
vector<int> left, right, order;
Mo(int N, int Q) : order(Q) {
width = max<int>(1, 1.0 * N / max<double>(1.0, sqrt(Q * 2.0 / 3.0)));
iota(begin(order), end(order), 0);
}
void insert(int l, int r) { /* [l, r) */
left.emplace_back(l);
right.emplace_back(r);
}
template <typename AL, typename AR, typename DL, typename DR, typename REM>
void run(const AL &add_left, const AR &add_right, const DL &delete_left,
const DR &delete_right, const REM &rem) {
assert(left.size() == order.size());
sort(begin(order), end(order), [&](int a, int b) {
int ablock = left[a] / width, bblock = left[b] / width;
if (ablock != bblock) return ablock < bblock;
if (ablock & 1) return right[a] < right[b];
return right[a] > right[b];
});
int nl = 0, nr = 0;
for (auto idx : order) {
while (nl > left[idx]) add_left(--nl);
while (nr < right[idx]) add_right(nr++);
while (nl < left[idx]) delete_left(nl++);
while (nr > right[idx]) delete_right(--nr);
rem(idx);
}
}
};
/**
* @brief Mo's algorithm
* @docs docs/misc/mo.md
*/
//
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(r * mod == 1, "invalid, r * mod != 1");
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const { return pow(mod - 2); }
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
template <typename T>
struct Binomial {
vector<T> f, g, h;
Binomial(int MAX = 0) {
assert(T::get_mod() != 0 && "Binomial<mint>()");
f.resize(1, T{1});
g.resize(1, T{1});
h.resize(1, T{1});
while (MAX >= (int)f.size()) extend();
}
void extend() {
int n = f.size();
int m = n * 2;
f.resize(m);
g.resize(m);
h.resize(m);
for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);
g[m - 1] = f[m - 1].inverse();
h[m - 1] = g[m - 1] * f[m - 2];
for (int i = m - 2; i >= n; i--) {
g[i] = g[i + 1] * T(i + 1);
h[i] = g[i] * f[i - 1];
}
}
T fac(int i) {
if (i < 0) return T(0);
while (i >= (int)f.size()) extend();
return f[i];
}
T finv(int i) {
if (i < 0) return T(0);
while (i >= (int)g.size()) extend();
return g[i];
}
T inv(int i) {
if (i < 0) return -inv(-i);
while (i >= (int)h.size()) extend();
return h[i];
}
T C(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
return fac(n) * finv(n - r) * finv(r);
}
inline T operator()(int n, int r) { return C(n, r); }
template <typename I>
T multinomial(const vector<I>& r) {
static_assert(is_integral<I>::value == true);
int n = 0;
for (auto& x : r) {
if (x < 0) return T(0);
n += x;
}
T res = fac(n);
for (auto& x : r) res *= finv(x);
return res;
}
template <typename I>
T operator()(const vector<I>& r) {
return multinomial(r);
}
T C_naive(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
T ret = T(1);
r = min(r, n - r);
for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);
return ret;
}
T P(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
return fac(n) * finv(n - r);
}
// [x^r] 1 / (1-x)^n
T H(int n, int r) {
if (n < 0 || r < 0) return T(0);
return r == 0 ? 1 : C(n + r - 1, r);
}
};
//
using namespace Nyaan;
using mint = LazyMontgomeryModInt<998244353>;
// using mint = LazyMontgomeryModInt<1000000007>;
using vm = vector<mint>;
using vvm = vector<vm>;
Binomial<mint> C{200003};
using namespace Nyaan;
void q() {
int Q;
rd(Q);
V<pi> qs(Q);
rep(i, Q) {
rd(qs[i].fi, qs[i].se);
--qs[i].fi, --qs[i].se;
}
int N = 2;
for (auto& p : qs) N = max(N, p.first);
Binomial<mint> b(N + 1);
Fast_Mo mo(N, Q);
for (auto& p : qs) {
assert(p.second <= p.first);
assert(p.first <= N);
mo.insert(p.second, p.first);
}
vector<mint> ans(Q);
mint cur = 1, inv2 = mint{2}.inverse();
int n = 0, m = 0;
auto al = [&](int) { cur -= b.C(n, m--); };
auto ar = [&](int) { cur += cur - b.C(n++, m); };
auto el = [&](int) { cur += b.C(n, ++m); };
auto er = [&](int) { cur = (cur + b.C(--n, m)) * inv2; };
auto q = [&](int i) { ans[i] = cur; };
mo.run(al, ar, el, er, q);
vm pw(N + 2);
pw[0] = 1;
rep1(i, N + 1) pw[i] = pw[i - 1] + pw[i - 1];
rep(i, Q) wtn((ans[i] * (pw[qs[i].fi + 1] - 1)).get());
}
void Nyaan::solve() {
int t = 1;
// in(t);
while (t--) q();
}