#include <iostream>
#include <vector>
using namespace std;
using ll = long long;
using pll = pair<ll, ll>;
constexpr ll MOD = 1e9+7;
ll pow(ll a, ll b);
ll inv(ll a) {return pow(a, MOD-2);}
int main()
{
cin.tie(0)->sync_with_stdio();
int n, q;
cin>>n>>q;
vector<pll> vec;
vec.reserve(n+1);
vec.resize(n);
for(auto& [x, y] : vec)
cin>>x>>y;
vec.push_back({0, 1});
++n;
vector<pll> pref(n+1);
pref[0] = {0, 1};
auto naive_merge = [](const pll& u, const pll& v) {
auto [c, d] = u;
auto [a, b] = v;
if(b == 1)
return pll{(c+a) % MOD, d};
else
return pll{(c*b) % MOD, (d*b) % MOD};
};
for(int i=0; i<n; i++) {
pref[i+1] = naive_merge(pref[i], vec[i]);
}
vector<int> nextz(n);
vector<pll> nextz2(n);
vector<bool> nextz3(n);
nextz[n-1] = n-1;
nextz2[n-1] = {0, 0};
for(int i=n-2; i>=0; i--) {
if((vec[i+1].first != 0) && (vec[i+1].second != 1)) {
nextz[i] = i+1;
nextz2[i] = {0, 1};
nextz3[i] = 0;
} else {
nextz[i] = nextz[i+1];
// nextz2[i] = /*merge n2[i+1] o vec[i+1]*/
auto [c, d] = nextz2[i+1];
auto [a, b] = vec[i+1];
if(b == 1) {
nextz2[i] = pll{(c+a*d) % MOD, d};
nextz3[i] = nextz3[i+1] || (c+a*d >= MOD);
}
else {
nextz2[i] = pll{c, (d*b) % MOD};
nextz3[i] = nextz3[i+1] || (d*b >= MOD);
}
}
}
/*
for(int i=0; i<n+1; i++) {
cout<<i<<":\t"<<pref[i].first<<"\t"<<pref[i].second;
if(i != n)
cout<<"\t"<<nextz[i]<<";\t"<<nextz2[i].first<<"\t"<<nextz2[i].second
<<"\t("<<nextz3[i]<<")\t";
cout<<"\n";
}
*/
while(q--) {
ll x, l, r;
cin>>x>>l>>r;
while(1) {
// cout<<"Have (x, l, r) = ("<<x<<", "<<l<<", "<<r<<")\n";
x = max(vec[l].first + x, vec[l].second * x);
if(x >= MOD) {
x %= MOD;
++l;
break;
}
if((nextz[l] >= r) || (nextz3[l])) {
++l;
break;
}
x = nextz2[l].first + x * nextz2[l].second;
l = nextz[l];
if(x >= MOD) {
x %= MOD;
break;
}
} //x is overflown, l is ++ed
// cout<<"Now (x, l, r) = ("<<x<<", "<<l<<", "<<r<<")\n";
auto [a, b] = pref[r];
auto [c, d] = pref[l];
ll e = b * inv(d) % MOD;
ll f = ((a - c*e) % MOD + MOD) % MOD;
// cout<<"("<<f<<", "<<e<<")\n";
// cout<<b<<","<<d<<","<<e<<"\n";
x = (x*e + f) % MOD;
cout<<x<<"\n";
}
}
ll pow(ll a, ll b) {
if(b == 0)
return 1;
if(b&1)
return a * pow(a*a % MOD, b/2) % MOD;
return pow(a*a % MOD, b/2);
}
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 | #include <iostream> #include <vector> using namespace std; using ll = long long; using pll = pair<ll, ll>; constexpr ll MOD = 1e9+7; ll pow(ll a, ll b); ll inv(ll a) {return pow(a, MOD-2);} int main() { cin.tie(0)->sync_with_stdio(); int n, q; cin>>n>>q; vector<pll> vec; vec.reserve(n+1); vec.resize(n); for(auto& [x, y] : vec) cin>>x>>y; vec.push_back({0, 1}); ++n; vector<pll> pref(n+1); pref[0] = {0, 1}; auto naive_merge = [](const pll& u, const pll& v) { auto [c, d] = u; auto [a, b] = v; if(b == 1) return pll{(c+a) % MOD, d}; else return pll{(c*b) % MOD, (d*b) % MOD}; }; for(int i=0; i<n; i++) { pref[i+1] = naive_merge(pref[i], vec[i]); } vector<int> nextz(n); vector<pll> nextz2(n); vector<bool> nextz3(n); nextz[n-1] = n-1; nextz2[n-1] = {0, 0}; for(int i=n-2; i>=0; i--) { if((vec[i+1].first != 0) && (vec[i+1].second != 1)) { nextz[i] = i+1; nextz2[i] = {0, 1}; nextz3[i] = 0; } else { nextz[i] = nextz[i+1]; // nextz2[i] = /*merge n2[i+1] o vec[i+1]*/ auto [c, d] = nextz2[i+1]; auto [a, b] = vec[i+1]; if(b == 1) { nextz2[i] = pll{(c+a*d) % MOD, d}; nextz3[i] = nextz3[i+1] || (c+a*d >= MOD); } else { nextz2[i] = pll{c, (d*b) % MOD}; nextz3[i] = nextz3[i+1] || (d*b >= MOD); } } } /* for(int i=0; i<n+1; i++) { cout<<i<<":\t"<<pref[i].first<<"\t"<<pref[i].second; if(i != n) cout<<"\t"<<nextz[i]<<";\t"<<nextz2[i].first<<"\t"<<nextz2[i].second <<"\t("<<nextz3[i]<<")\t"; cout<<"\n"; } */ while(q--) { ll x, l, r; cin>>x>>l>>r; while(1) { // cout<<"Have (x, l, r) = ("<<x<<", "<<l<<", "<<r<<")\n"; x = max(vec[l].first + x, vec[l].second * x); if(x >= MOD) { x %= MOD; ++l; break; } if((nextz[l] >= r) || (nextz3[l])) { ++l; break; } x = nextz2[l].first + x * nextz2[l].second; l = nextz[l]; if(x >= MOD) { x %= MOD; break; } } //x is overflown, l is ++ed // cout<<"Now (x, l, r) = ("<<x<<", "<<l<<", "<<r<<")\n"; auto [a, b] = pref[r]; auto [c, d] = pref[l]; ll e = b * inv(d) % MOD; ll f = ((a - c*e) % MOD + MOD) % MOD; // cout<<"("<<f<<", "<<e<<")\n"; // cout<<b<<","<<d<<","<<e<<"\n"; x = (x*e + f) % MOD; cout<<x<<"\n"; } } ll pow(ll a, ll b) { if(b == 0) return 1; if(b&1) return a * pow(a*a % MOD, b/2) % MOD; return pow(a*a % MOD, b/2); } |
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