#include <bits/stdc++.h>
#define int long long
#define pi pair<int, int>
const int MOD = 1000000007;
using namespace std;
struct event{
int add;
int mul;
};
struct sum_range{
int n;
vector<int> values;
sum_range(const vector<event> &content){
n = content.size();
values.resize(n+1);
for(int i=1; i<=n; i++)
values[i] = values[i-1]+content[i-1].add; //we don't take modulo here on purpose
}
int query(int l, int r) { //[l r)
if(r<=l) return 0;
r = min(r, n);
l = max(l, 0LL);
return values[r]-values[l];
}
};
int fast_pow(int a, int k){
//assert(a!=0);
if(k==0) return 1;
if(a==0) return 0;
if(k%2==1) return (a*fast_pow(a, k-1))%MOD;
if(k%2==0) {
int value = fast_pow(a, k/2);
return (value*value)%MOD;
}
}
int inverse(int a){
return fast_pow(a, MOD-2);
}
struct mul_range{
int n;
vector<int> values;
mul_range(const vector<event> &content){
n = content.size();
values.resize(n+1, 1);
for(int i=1; i<=n; i++)
values[i] = (values[i-1]*content[i-1].mul)%MOD;
}
int query(int l, int r) { //[l r)
if(r<=l) return 1;
r = min(r, n);
l = max(l, 0LL);
return (values[r]*inverse(values[l]))%MOD;
}
};
struct effect{
int multiplier;
int constant;
};
struct best_inf_money{
int n;
vector<effect> values;
best_inf_money(const vector<event> & content){
n = content.size();
values.resize(n+1, {1, 0});
for(int i=1; i<=n; i++){
if(content[i-1].mul == 1){
values[i] = {values[i-1].multiplier, (values[i-1].constant + content[i-1].add)%MOD};
} else {
values[i] = {(content[i-1].mul*values[i-1].multiplier)%MOD, (content[i-1].mul *values[i-1].constant)%MOD};
}
}
}
effect query(int l, int r){
if(r<=l) return {1, 0};
r = min(r, n);
l = max(l, 0LL);
auto [a_1, b_1] = values[l];
auto [a_2, b_2] = values[r];
int alpha = (a_2 * inverse(a_1))%MOD;
int beta = (b_2-b_1*alpha);
beta -= (beta/MOD) * MOD;
beta += 5 * MOD;
beta %= MOD;
return {alpha, beta};
}
};
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
int n, q; cin >> n >> q;
vector<event> events(n);
for(auto &[a, m] : events)
cin >> a >> m;
set<int> non_trivial;
for(auto [index, element] : views::enumerate(events))
if(element.mul != 1)
non_trivial.insert(index);
non_trivial.insert(LLONG_MAX);
sum_range add_sum(events);
mul_range mul_prod(events);
best_inf_money best_func(events);
int cnt=0;
while(q--){
if(++cnt == 84){
cerr << "ser";
}
int x, l, r; cin >> x >> l >> r;
//rozwazamy [l, r)
bool overflowed=false;
auto next_non_trivial = non_trivial.upper_bound(l-1);
int result = x;
int current = l-1;
while(!overflowed && *next_non_trivial < r){
result += add_sum.query(current+1, *next_non_trivial);
auto overflowcheckbeforemod = [&](){
if(result >= MOD){
result%=MOD;
overflowed = true;
}
};
overflowcheckbeforemod();
auto [add, mul] = events[*next_non_trivial];
if(overflowed || result+add <= result*mul){
result*=mul;
overflowcheckbeforemod();
} else {
result+=add;
overflowcheckbeforemod();
}
current = *next_non_trivial;
next_non_trivial = non_trivial.upper_bound(current);
}
int non_triv_before_r = *non_trivial.lower_bound(r);
auto [a, b] = best_func.query(current+1, r);
((result*=a)+=b)%=MOD;
cout << result << '\n';
}
}
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 | #include <bits/stdc++.h> #define int long long #define pi pair<int, int> const int MOD = 1000000007; using namespace std; struct event{ int add; int mul; }; struct sum_range{ int n; vector<int> values; sum_range(const vector<event> &content){ n = content.size(); values.resize(n+1); for(int i=1; i<=n; i++) values[i] = values[i-1]+content[i-1].add; //we don't take modulo here on purpose } int query(int l, int r) { //[l r) if(r<=l) return 0; r = min(r, n); l = max(l, 0LL); return values[r]-values[l]; } }; int fast_pow(int a, int k){ //assert(a!=0); if(k==0) return 1; if(a==0) return 0; if(k%2==1) return (a*fast_pow(a, k-1))%MOD; if(k%2==0) { int value = fast_pow(a, k/2); return (value*value)%MOD; } } int inverse(int a){ return fast_pow(a, MOD-2); } struct mul_range{ int n; vector<int> values; mul_range(const vector<event> &content){ n = content.size(); values.resize(n+1, 1); for(int i=1; i<=n; i++) values[i] = (values[i-1]*content[i-1].mul)%MOD; } int query(int l, int r) { //[l r) if(r<=l) return 1; r = min(r, n); l = max(l, 0LL); return (values[r]*inverse(values[l]))%MOD; } }; struct effect{ int multiplier; int constant; }; struct best_inf_money{ int n; vector<effect> values; best_inf_money(const vector<event> & content){ n = content.size(); values.resize(n+1, {1, 0}); for(int i=1; i<=n; i++){ if(content[i-1].mul == 1){ values[i] = {values[i-1].multiplier, (values[i-1].constant + content[i-1].add)%MOD}; } else { values[i] = {(content[i-1].mul*values[i-1].multiplier)%MOD, (content[i-1].mul *values[i-1].constant)%MOD}; } } } effect query(int l, int r){ if(r<=l) return {1, 0}; r = min(r, n); l = max(l, 0LL); auto [a_1, b_1] = values[l]; auto [a_2, b_2] = values[r]; int alpha = (a_2 * inverse(a_1))%MOD; int beta = (b_2-b_1*alpha); beta -= (beta/MOD) * MOD; beta += 5 * MOD; beta %= MOD; return {alpha, beta}; } }; signed main(){ ios_base::sync_with_stdio(0); cin.tie(0); int n, q; cin >> n >> q; vector<event> events(n); for(auto &[a, m] : events) cin >> a >> m; set<int> non_trivial; for(auto [index, element] : views::enumerate(events)) if(element.mul != 1) non_trivial.insert(index); non_trivial.insert(LLONG_MAX); sum_range add_sum(events); mul_range mul_prod(events); best_inf_money best_func(events); int cnt=0; while(q--){ if(++cnt == 84){ cerr << "ser"; } int x, l, r; cin >> x >> l >> r; //rozwazamy [l, r) bool overflowed=false; auto next_non_trivial = non_trivial.upper_bound(l-1); int result = x; int current = l-1; while(!overflowed && *next_non_trivial < r){ result += add_sum.query(current+1, *next_non_trivial); auto overflowcheckbeforemod = [&](){ if(result >= MOD){ result%=MOD; overflowed = true; } }; overflowcheckbeforemod(); auto [add, mul] = events[*next_non_trivial]; if(overflowed || result+add <= result*mul){ result*=mul; overflowcheckbeforemod(); } else { result+=add; overflowcheckbeforemod(); } current = *next_non_trivial; next_non_trivial = non_trivial.upper_bound(current); } int non_triv_before_r = *non_trivial.lower_bound(r); auto [a, b] = best_func.query(current+1, r); ((result*=a)+=b)%=MOD; cout << result << '\n'; } } |
English