#include <bits/stdc++.h>
using namespace std;
constexpr int mod = 1e9 + 7;
inline int add(int a, int b) {
a += b;
return (a >= mod) ? a - mod : a;
}
inline int mul(int a, int b) {
return static_cast<int>(a * static_cast<long long>(b) % mod);
}
class Points {
public:
Points(int res) : res_(res) {}
Points(long long res) : res_(res % mod), big_(res >= mod) {}
Points& operator+=(const Points& other) {
big_ |= other.big_ | (res_ + other.res_ >= mod);
res_ = add(res_, other.res_);
return (*this);
}
friend Points operator+(Points lhs, const Points& rhs) {
lhs += rhs;
return lhs;
}
Points& operator*=(const Points& other) {
big_ = (res_ > 0 && other.res_ > 0) && (big_ || other.big_ || res_ >= (mod + other.res_ - 1) / other.res_);
res_ = mul(res_, other.res_);
return (*this);
}
friend Points operator*(Points lhs, const Points& rhs) {
lhs *= rhs;
return lhs;
}
Points& apply(int a, int b) {
// cerr << "[APPLY] " << res_ << ", " << a << ", " << b << endl;
if (b == 1) {
// cerr << "b == 1" << endl;
return (*this) += a;
}
if (big_) {
// cerr << "WEIRD" << endl;
return (*this) *= b;
}
if ((mod + b - 1) / b <= res_) {
// cerr << "BIG MOD" << endl;
return (*this) *= b;
}
if (res_ + a >= res_ * b) {
// cerr << "ADDITION?" << endl;
return (*this) += a;
}
else {
// cerr << "REALLY WEIRD" << endl;
return (*this) *= b;
}
}
friend ostream& operator<<(ostream& os, const Points& pts) {
return os << "[DEBUG]: Points(" << pts.res_ << ", " << pts.big_ << "), ";
}
bool nice_to_mul() const {
return res_ != 1 || big_;
}
bool is_big() const {
return big_;
}
int operator()() const {
return res_;
}
private:
int res_;
bool big_ = false;
};
class Function {
public:
static Function from_add(const Points& val) {
return Function(1, val);
}
static Function from_mul(const Points& val) {
return Function(val, 0);
}
Function() : a_(1), b_(0) {}
friend Function combine(const Function& lhs, const Function& rhs) {
// cerr << "combine(" << lhs << ", " << rhs << ")" << endl;
auto func = Function(lhs.a_ * rhs.a_, lhs.b_ * rhs.a_ + rhs.b_);
// cerr << "result = " << func << endl;
return func;
}
Points operator()(const Points& x) {
return a_ * x + b_;
}
friend ostream& operator<<(ostream& os, const Function& func) {
return os << "[DEBUG] Function(" << func.a_ << ", " << func.b_ << "), ";
}
private:
Points a_, b_;
explicit Function(const Points& a, const Points& b) : a_(a), b_(b) {}
};
class FastEvaluator {
public:
explicit FastEvaluator(const vector<pair<int, int>>& arr) {
ss_ = 1;
while (ss_ < (int) arr.size()) {
ss_ *= 2;
}
tree_.resize(2 * ss_);
for (int i = 0; i < (int) arr.size(); i++) {
if (arr[i].second > 1) {
tree_[ss_ + i] = Function::from_mul(arr[i].second);
}
else {
tree_[ss_ + i] = Function::from_add(arr[i].first);
}
// cerr << "PUTTING " << i << " " << tree_[ss_ + i] << endl;
}
for (int i = ss_-1; i > 0; i--) {
tree_[i] = combine(tree_[i*2], tree_[i*2+1]);
// cerr << "COMBINED " << i << " " << tree_[i] << endl;
}
}
Function aggregate(int l, int r) const {
return aggregate(l, r, 0, ss_-1, 1);
}
private:
Function aggregate(int a, int b, int l, int r, int x) const {
if (a <= l && r <= b) {
// cerr << "HEY! I have been there " << a << " " << b << " " << l << " " << r << " " << tree_[x] << endl;
return tree_[x];
}
int mid = (l + r) / 2;
Function res;
if (a <= mid) {
res = combine(res, aggregate(a, b, l, mid, x*2));
}
if (mid < b) {
res = combine(res, aggregate(a, b, mid+1, r, x*2+1));
}
// cerr << "AGGREGATE(" << l << ", " << r << ") = " << res << endl;
return res;
}
private:
int ss_;
vector<Function> tree_;
};
class SafeWalker {
public:
explicit SafeWalker(const vector<pair<int, int>>& arr) : ptr_(arr.size(), arr.size()), pref_(arr.size() + 1) {
int wh = arr.size();
for (int i = (int)arr.size()-1; i >= 0; i--) {
if (arr[i].second == 1) {
ptr_[i] = wh;
pref_[i+1] = arr[i].first;
}
else {
ptr_[i] = i;
wh = i;
}
}
for (int i = 1; i <= arr.size(); i++) {
pref_[i] += pref_[i-1];
}
}
Points get_points(int l, int r) const {
return pref_[r + 1] - pref_[l];
}
pair<Points, int> operator()(int wh, int bound) const {
int dst = min(ptr_[wh], bound+1);
return make_pair(get_points(wh, dst-1), dst) ;
}
private:
vector<int> ptr_;
vector<long long> pref_;
};
class UselessAvoider {
public:
explicit UselessAvoider(const vector<pair<int, int>>& arr) : ptr_(arr.size(), arr.size()) {
int wh = arr.size();
for (int i = (int)arr.size()-1; i >= 0; i--) {
if (arr[i].second == 1 && arr[i].first == 0) {
ptr_[i] = wh;
}
else {
ptr_[i] = i;
wh = i;
}
}
}
int operator()(int wh, int bound) const {
return min(ptr_[wh], bound+1);
}
private:
vector<int> ptr_;
vector<long long> pref_;
};
void solve(int x, int l, int r, const vector<pair<int, int>>& arr, const SafeWalker& safe_walker,
const FastEvaluator& fast_evaluator, const UselessAvoider& useless_avoider) {
Points points(x);
// cerr << "STARTING " << l << " " << r << endl;
l = useless_avoider(l, r);
// cerr << "AVOIDED " << l << " " << r << endl;
if (l <= r) {
points.apply(arr[l].first, arr[l].second);
// cerr << points << endl;
l++;
}
while (l <= r && !points.is_big()) {
auto [add, wh] = safe_walker(l, r);
points += add;
l = wh;
// cerr << points << l << endl;
if (l <= r) {
points.apply(arr[l].first, arr[l].second);
// cerr << points << endl;
l++;
}
}
if (l <= r) {
// cerr << "ALL " << l << " " << r << endl;
Function func = fast_evaluator.aggregate(l, r);
// cerr << func << endl;
points = func(points);
// cerr << points << endl;
}
cout << points() << "\n";
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
int n, q;
cin >> n >> q;
vector<pair<int, int>> arr(n);
for (auto& [a, b] : arr) {
cin >> a >> b;
}
const SafeWalker safe_walker(arr);
const FastEvaluator fast_evaluator(arr);
const UselessAvoider useless_avoider(arr);
while (q--) {
int x, l, r;
cin >> x >> l >> r;
r--;
solve(x, l, r, arr, safe_walker, fast_evaluator, useless_avoider);
}
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 | #include <bits/stdc++.h> using namespace std; constexpr int mod = 1e9 + 7; inline int add(int a, int b) { a += b; return (a >= mod) ? a - mod : a; } inline int mul(int a, int b) { return static_cast<int>(a * static_cast<long long>(b) % mod); } class Points { public: Points(int res) : res_(res) {} Points(long long res) : res_(res % mod), big_(res >= mod) {} Points& operator+=(const Points& other) { big_ |= other.big_ | (res_ + other.res_ >= mod); res_ = add(res_, other.res_); return (*this); } friend Points operator+(Points lhs, const Points& rhs) { lhs += rhs; return lhs; } Points& operator*=(const Points& other) { big_ = (res_ > 0 && other.res_ > 0) && (big_ || other.big_ || res_ >= (mod + other.res_ - 1) / other.res_); res_ = mul(res_, other.res_); return (*this); } friend Points operator*(Points lhs, const Points& rhs) { lhs *= rhs; return lhs; } Points& apply(int a, int b) { // cerr << "[APPLY] " << res_ << ", " << a << ", " << b << endl; if (b == 1) { // cerr << "b == 1" << endl; return (*this) += a; } if (big_) { // cerr << "WEIRD" << endl; return (*this) *= b; } if ((mod + b - 1) / b <= res_) { // cerr << "BIG MOD" << endl; return (*this) *= b; } if (res_ + a >= res_ * b) { // cerr << "ADDITION?" << endl; return (*this) += a; } else { // cerr << "REALLY WEIRD" << endl; return (*this) *= b; } } friend ostream& operator<<(ostream& os, const Points& pts) { return os << "[DEBUG]: Points(" << pts.res_ << ", " << pts.big_ << "), "; } bool nice_to_mul() const { return res_ != 1 || big_; } bool is_big() const { return big_; } int operator()() const { return res_; } private: int res_; bool big_ = false; }; class Function { public: static Function from_add(const Points& val) { return Function(1, val); } static Function from_mul(const Points& val) { return Function(val, 0); } Function() : a_(1), b_(0) {} friend Function combine(const Function& lhs, const Function& rhs) { // cerr << "combine(" << lhs << ", " << rhs << ")" << endl; auto func = Function(lhs.a_ * rhs.a_, lhs.b_ * rhs.a_ + rhs.b_); // cerr << "result = " << func << endl; return func; } Points operator()(const Points& x) { return a_ * x + b_; } friend ostream& operator<<(ostream& os, const Function& func) { return os << "[DEBUG] Function(" << func.a_ << ", " << func.b_ << "), "; } private: Points a_, b_; explicit Function(const Points& a, const Points& b) : a_(a), b_(b) {} }; class FastEvaluator { public: explicit FastEvaluator(const vector<pair<int, int>>& arr) { ss_ = 1; while (ss_ < (int) arr.size()) { ss_ *= 2; } tree_.resize(2 * ss_); for (int i = 0; i < (int) arr.size(); i++) { if (arr[i].second > 1) { tree_[ss_ + i] = Function::from_mul(arr[i].second); } else { tree_[ss_ + i] = Function::from_add(arr[i].first); } // cerr << "PUTTING " << i << " " << tree_[ss_ + i] << endl; } for (int i = ss_-1; i > 0; i--) { tree_[i] = combine(tree_[i*2], tree_[i*2+1]); // cerr << "COMBINED " << i << " " << tree_[i] << endl; } } Function aggregate(int l, int r) const { return aggregate(l, r, 0, ss_-1, 1); } private: Function aggregate(int a, int b, int l, int r, int x) const { if (a <= l && r <= b) { // cerr << "HEY! I have been there " << a << " " << b << " " << l << " " << r << " " << tree_[x] << endl; return tree_[x]; } int mid = (l + r) / 2; Function res; if (a <= mid) { res = combine(res, aggregate(a, b, l, mid, x*2)); } if (mid < b) { res = combine(res, aggregate(a, b, mid+1, r, x*2+1)); } // cerr << "AGGREGATE(" << l << ", " << r << ") = " << res << endl; return res; } private: int ss_; vector<Function> tree_; }; class SafeWalker { public: explicit SafeWalker(const vector<pair<int, int>>& arr) : ptr_(arr.size(), arr.size()), pref_(arr.size() + 1) { int wh = arr.size(); for (int i = (int)arr.size()-1; i >= 0; i--) { if (arr[i].second == 1) { ptr_[i] = wh; pref_[i+1] = arr[i].first; } else { ptr_[i] = i; wh = i; } } for (int i = 1; i <= arr.size(); i++) { pref_[i] += pref_[i-1]; } } Points get_points(int l, int r) const { return pref_[r + 1] - pref_[l]; } pair<Points, int> operator()(int wh, int bound) const { int dst = min(ptr_[wh], bound+1); return make_pair(get_points(wh, dst-1), dst) ; } private: vector<int> ptr_; vector<long long> pref_; }; class UselessAvoider { public: explicit UselessAvoider(const vector<pair<int, int>>& arr) : ptr_(arr.size(), arr.size()) { int wh = arr.size(); for (int i = (int)arr.size()-1; i >= 0; i--) { if (arr[i].second == 1 && arr[i].first == 0) { ptr_[i] = wh; } else { ptr_[i] = i; wh = i; } } } int operator()(int wh, int bound) const { return min(ptr_[wh], bound+1); } private: vector<int> ptr_; vector<long long> pref_; }; void solve(int x, int l, int r, const vector<pair<int, int>>& arr, const SafeWalker& safe_walker, const FastEvaluator& fast_evaluator, const UselessAvoider& useless_avoider) { Points points(x); // cerr << "STARTING " << l << " " << r << endl; l = useless_avoider(l, r); // cerr << "AVOIDED " << l << " " << r << endl; if (l <= r) { points.apply(arr[l].first, arr[l].second); // cerr << points << endl; l++; } while (l <= r && !points.is_big()) { auto [add, wh] = safe_walker(l, r); points += add; l = wh; // cerr << points << l << endl; if (l <= r) { points.apply(arr[l].first, arr[l].second); // cerr << points << endl; l++; } } if (l <= r) { // cerr << "ALL " << l << " " << r << endl; Function func = fast_evaluator.aggregate(l, r); // cerr << func << endl; points = func(points); // cerr << points << endl; } cout << points() << "\n"; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); int n, q; cin >> n >> q; vector<pair<int, int>> arr(n); for (auto& [a, b] : arr) { cin >> a >> b; } const SafeWalker safe_walker(arr); const FastEvaluator fast_evaluator(arr); const UselessAvoider useless_avoider(arr); while (q--) { int x, l, r; cin >> x >> l >> r; r--; solve(x, l, r, arr, safe_walker, fast_evaluator, useless_avoider); } } |
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