// Template generated by Clank
#include<bits/stdc++.h>
using namespace std;
#define st first
#define nd second
#define all(x) x.begin(), x.end()
#define BOOST cin.tie(NULL); ios_base::sync_with_stdio(false);
// #define int ll
typedef long long ll;
ll mod = 1e9 + 7;
int n, q;
vector<pair<ll, ll>> events;
vector<ll> sum;
vector<ll> prod;
vector<ll> next_prod_eqm2;
vector<ll> weird_sum;
ll ssum(ll l, ll r, int app_mod=1){
if(l > r) return 0;
if(app_mod){
return (mod + sum[r] - sum[l - 1]) % mod;
} else {
return sum[r] - sum[l - 1];
}
}
// ll fastpow(ll a, ll k){
// if(k == 0) return 1;
// ll tmp = fastpow(a, k/2);
// if(k&1) return (((tmp * tmp) % mod) * a) % mod;
// else return (tmp * tmp) % mod;
// }
ll fastpow(ll a, ll k){
ll res = 1;
while(k > 0){
if(k & 1) res = (res * a) % mod;
a = (a * a) % mod;
k >>= 1;
}
return res;
}
ll rev(ll x){
return fastpow(x, mod - 2);
}
ll sprod(ll l, ll r){
if(r < l) return 1;
return (prod[r] * rev(prod[l - 1])) % mod;
}
void solve(){
ll x, l, r;
cin >> x >> l >> r;
// l++;
// r++;
ll plus_jump;
while(x <= mod && l < r){
plus_jump = min(r, next_prod_eqm2[l]);
x += ssum(l + 1, plus_jump - 1, 0);
l = plus_jump;
if(x > mod){
l--;
break;
}
if(x + events[l].st > x * events[l].nd){
x += events[l].st;
} else {
x *= events[l].nd;
}
}
// cout << x << "\n";
// cout << l << " " << r << "\n";
x %= mod;
if(l == r){
cout << x << "\n";
return;
}
// cout << sprod(l + 1, r) << "\n";
ll ans = (x * sprod(l + 1, r)) % mod;
// cout << ans << "\n";
ll ans2 = (weird_sum[l + 1] - weird_sum[r + 1] + mod) % mod;
// cout << ans2 << "\n";
ans2 = (ans2 * rev(sprod(r + 1, n))) % mod;
// cout << ans2 << "\n";
ans = (ans + ans2) % mod;
cout << ans << "\n";
return;
}
int32_t main(){
// cout << fastpow(2,10) << " " << rev(2546234) << " test\n";
BOOST;
cin >> n >> q;
events.resize(n + 2);
sum.resize(n + 2);
prod.resize(n + 2);
next_prod_eqm2.resize(n + 2);
weird_sum.resize(n + 2);
prod[0] = 1;
for(int i = 1; i <= n; i++){
cin >> events[i].st >> events[i].nd;
sum[i] = sum[i - 1] + events[i].st;
prod[i] = (prod[i - 1] * max(events[i].nd, 1LL)) % mod;
}
int last = n + 1;
for(int i = n + 1; i >= 0; i--){
next_prod_eqm2[i] = last;
if(events[i].nd > 1) last = i;
}
ll multi = 1;
for(int i = n; i >= 0; i--){
weird_sum[i] = weird_sum[i + 1];
if(events[i].nd > 1){
multi = (multi * events[i].nd) % mod;
} else {
weird_sum[i] = (weird_sum[i] + events[i].st * multi) % mod;
}
}
while(q--){
solve();
}
return 0;
}
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 | // Template generated by Clank #include<bits/stdc++.h> using namespace std; #define st first #define nd second #define all(x) x.begin(), x.end() #define BOOST cin.tie(NULL); ios_base::sync_with_stdio(false); // #define int ll typedef long long ll; ll mod = 1e9 + 7; int n, q; vector<pair<ll, ll>> events; vector<ll> sum; vector<ll> prod; vector<ll> next_prod_eqm2; vector<ll> weird_sum; ll ssum(ll l, ll r, int app_mod=1){ if(l > r) return 0; if(app_mod){ return (mod + sum[r] - sum[l - 1]) % mod; } else { return sum[r] - sum[l - 1]; } } // ll fastpow(ll a, ll k){ // if(k == 0) return 1; // ll tmp = fastpow(a, k/2); // if(k&1) return (((tmp * tmp) % mod) * a) % mod; // else return (tmp * tmp) % mod; // } ll fastpow(ll a, ll k){ ll res = 1; while(k > 0){ if(k & 1) res = (res * a) % mod; a = (a * a) % mod; k >>= 1; } return res; } ll rev(ll x){ return fastpow(x, mod - 2); } ll sprod(ll l, ll r){ if(r < l) return 1; return (prod[r] * rev(prod[l - 1])) % mod; } void solve(){ ll x, l, r; cin >> x >> l >> r; // l++; // r++; ll plus_jump; while(x <= mod && l < r){ plus_jump = min(r, next_prod_eqm2[l]); x += ssum(l + 1, plus_jump - 1, 0); l = plus_jump; if(x > mod){ l--; break; } if(x + events[l].st > x * events[l].nd){ x += events[l].st; } else { x *= events[l].nd; } } // cout << x << "\n"; // cout << l << " " << r << "\n"; x %= mod; if(l == r){ cout << x << "\n"; return; } // cout << sprod(l + 1, r) << "\n"; ll ans = (x * sprod(l + 1, r)) % mod; // cout << ans << "\n"; ll ans2 = (weird_sum[l + 1] - weird_sum[r + 1] + mod) % mod; // cout << ans2 << "\n"; ans2 = (ans2 * rev(sprod(r + 1, n))) % mod; // cout << ans2 << "\n"; ans = (ans + ans2) % mod; cout << ans << "\n"; return; } int32_t main(){ // cout << fastpow(2,10) << " " << rev(2546234) << " test\n"; BOOST; cin >> n >> q; events.resize(n + 2); sum.resize(n + 2); prod.resize(n + 2); next_prod_eqm2.resize(n + 2); weird_sum.resize(n + 2); prod[0] = 1; for(int i = 1; i <= n; i++){ cin >> events[i].st >> events[i].nd; sum[i] = sum[i - 1] + events[i].st; prod[i] = (prod[i - 1] * max(events[i].nd, 1LL)) % mod; } int last = n + 1; for(int i = n + 1; i >= 0; i--){ next_prod_eqm2[i] = last; if(events[i].nd > 1) last = i; } ll multi = 1; for(int i = n; i >= 0; i--){ weird_sum[i] = weird_sum[i + 1]; if(events[i].nd > 1){ multi = (multi * events[i].nd) % mod; } else { weird_sum[i] = (weird_sum[i] + events[i].st * multi) % mod; } } while(q--){ solve(); } return 0; } |
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