#include <bits/stdc++.h>
using namespace std;
#define fors(u, n, s) for(int u = (s); u<(n); u++)
#define foru(u, n) fors(u, n, 0)
#define f first
#define s second
#define vec vector
#define pb push_back
#define sz(x) ((int)x.size())
typedef long long ll;
#define debug(x) cout << __LINE__ << " | " << x << endl
// #define debug(x) {}
const int MOD = 1e9+7;
struct Modular {
int value;
Modular(long long v = 0) { value = v % MOD; }
Modular(long long a, long long b) : value(0){ *this += a; *this /= b;}
Modular& operator+=(Modular const& b) {value += b.value; if (value >= MOD) value -= MOD; return *this;}
Modular& operator-=(Modular const& b) {value -= b.value; if (value < 0) value += MOD;return *this;}
Modular& operator*=(Modular const& b) {value = (long long)value * b.value % MOD;return *this;}
friend Modular mexp(Modular a, long long e) {
Modular res = 1; while (e) { if (e&1) res *= a; a *= a; e >>= 1; }
return res;
}
friend Modular inverse(Modular a) { return mexp(a, MOD - 2); }
Modular& operator/=(Modular const& b) { return *this *= inverse(b); }
friend Modular operator+(Modular a, Modular const b) { return a += b; }
friend Modular operator-(Modular a, Modular const b) { return a -= b; }
friend Modular operator-(Modular const a) { return 0 - a; }
friend Modular operator*(Modular a, Modular const b) { return a *= b; }
friend Modular operator/(Modular a, Modular const b) { return a /= b; }
friend std::ostream& operator<<(std::ostream& os, Modular const& a) {return os << a.value;}
friend bool operator==(Modular const& a, Modular const& b) {return a.value == b.value;}
friend bool operator!=(Modular const& a, Modular const& b) {return a.value != b.value;}
};
struct linear{
Modular a;
Modular b;
linear() {}
linear(int a_, int b_) : a(Modular(a_)), b(Modular(b_)) {}
linear(Modular a_, Modular b_) : a(a_), b(b_) {}
friend linear operator+(const linear &l, const linear &r){
// l(x) = l.a*x + l.b
// r(x) = r.a*x + r.b
// r(l(x)) = r(l.a x + l.b) = r.a l.a x + r.a l.b + r.b
return linear(r.a * l.a, r.a*l.b + r.b);
}
friend linear inv(const linear &f){
// f(out(x)) = x
// a * out x + b = x
// a (out.a x + out.b) + b = x
// a out.a x + a out.b + b = x
// x (a out.a - 1) + (a out.b + b) = 0
// out.a = inv(a), out.b = -b/a
return linear(inverse(f.a), -f.b/f.a);
}
friend linear operator-(const linear &l, const linear &r){
return inv(l)+r;
}
Modular operator[](Modular x){
return a*x+b;
}
ll eval_ll(ll x){
return ((ll)a.value)*x+((ll)b.value);
}
};
struct fn{
ll plus;
linear a, b;
bool type; // 0 - plus, 1 - bi
};
const int N = 6e5;
fn v[N];
int next_bi[N];
ll pref[N];
linear pref_linear[N];
Modular querry(ll x, int l, int r){
while(true){
if(l == r) return Modular(x);
if(next_bi[l] >= r){
return Modular(x + pref[r] - pref[l]);
}
int jmp = next_bi[l];
x += pref[jmp]-pref[l];
l = jmp;
if(x >= MOD) return Modular((pref_linear[l]-pref_linear[r])[x]);
x = max(
v[l].a.eval_ll(x),
v[l].b.eval_ll(x)
);
l += 1;
if(x >= MOD) return Modular((pref_linear[l]-pref_linear[r])[x]);
}
}
void solve() {
int n, q; cin >> n >> q;
foru(i, n){
int a, b; cin >> a >> b;
if(b == 1){
v[i].plus = a;
v[i].a = linear(1, a);
v[i].type = false;
} else {
v[i].plus = 0;
v[i].a = linear(b, 0);
v[i].b = linear(1, a);
v[i].type = true;
}
}
next_bi[n] = n;
for(int i = n-1; i>=0; i--){
if(v[i].type) next_bi[i] = i;
else next_bi[i] = next_bi[i+1];
}
pref[0] = 0;
foru(i, n) pref[i+1] = pref[i] + v[i].plus;
pref_linear[0] = linear(1, 0);
foru(i, n) pref_linear[i+1] = pref_linear[i] + v[i].a;
foru(_i, q){
ll x; int l, r;
cin >> x >> l >> r;
cout << querry(x, l, r) << endl;
}
}
int main()
{
cin.tie(0); cout.tie(0);
ios_base::sync_with_stdio(0);
srand(time(NULL));
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 | #include <bits/stdc++.h> using namespace std; #define fors(u, n, s) for(int u = (s); u<(n); u++) #define foru(u, n) fors(u, n, 0) #define f first #define s second #define vec vector #define pb push_back #define sz(x) ((int)x.size()) typedef long long ll; #define debug(x) cout << __LINE__ << " | " << x << endl // #define debug(x) {} const int MOD = 1e9+7; struct Modular { int value; Modular(long long v = 0) { value = v % MOD; } Modular(long long a, long long b) : value(0){ *this += a; *this /= b;} Modular& operator+=(Modular const& b) {value += b.value; if (value >= MOD) value -= MOD; return *this;} Modular& operator-=(Modular const& b) {value -= b.value; if (value < 0) value += MOD;return *this;} Modular& operator*=(Modular const& b) {value = (long long)value * b.value % MOD;return *this;} friend Modular mexp(Modular a, long long e) { Modular res = 1; while (e) { if (e&1) res *= a; a *= a; e >>= 1; } return res; } friend Modular inverse(Modular a) { return mexp(a, MOD - 2); } Modular& operator/=(Modular const& b) { return *this *= inverse(b); } friend Modular operator+(Modular a, Modular const b) { return a += b; } friend Modular operator-(Modular a, Modular const b) { return a -= b; } friend Modular operator-(Modular const a) { return 0 - a; } friend Modular operator*(Modular a, Modular const b) { return a *= b; } friend Modular operator/(Modular a, Modular const b) { return a /= b; } friend std::ostream& operator<<(std::ostream& os, Modular const& a) {return os << a.value;} friend bool operator==(Modular const& a, Modular const& b) {return a.value == b.value;} friend bool operator!=(Modular const& a, Modular const& b) {return a.value != b.value;} }; struct linear{ Modular a; Modular b; linear() {} linear(int a_, int b_) : a(Modular(a_)), b(Modular(b_)) {} linear(Modular a_, Modular b_) : a(a_), b(b_) {} friend linear operator+(const linear &l, const linear &r){ // l(x) = l.a*x + l.b // r(x) = r.a*x + r.b // r(l(x)) = r(l.a x + l.b) = r.a l.a x + r.a l.b + r.b return linear(r.a * l.a, r.a*l.b + r.b); } friend linear inv(const linear &f){ // f(out(x)) = x // a * out x + b = x // a (out.a x + out.b) + b = x // a out.a x + a out.b + b = x // x (a out.a - 1) + (a out.b + b) = 0 // out.a = inv(a), out.b = -b/a return linear(inverse(f.a), -f.b/f.a); } friend linear operator-(const linear &l, const linear &r){ return inv(l)+r; } Modular operator[](Modular x){ return a*x+b; } ll eval_ll(ll x){ return ((ll)a.value)*x+((ll)b.value); } }; struct fn{ ll plus; linear a, b; bool type; // 0 - plus, 1 - bi }; const int N = 6e5; fn v[N]; int next_bi[N]; ll pref[N]; linear pref_linear[N]; Modular querry(ll x, int l, int r){ while(true){ if(l == r) return Modular(x); if(next_bi[l] >= r){ return Modular(x + pref[r] - pref[l]); } int jmp = next_bi[l]; x += pref[jmp]-pref[l]; l = jmp; if(x >= MOD) return Modular((pref_linear[l]-pref_linear[r])[x]); x = max( v[l].a.eval_ll(x), v[l].b.eval_ll(x) ); l += 1; if(x >= MOD) return Modular((pref_linear[l]-pref_linear[r])[x]); } } void solve() { int n, q; cin >> n >> q; foru(i, n){ int a, b; cin >> a >> b; if(b == 1){ v[i].plus = a; v[i].a = linear(1, a); v[i].type = false; } else { v[i].plus = 0; v[i].a = linear(b, 0); v[i].b = linear(1, a); v[i].type = true; } } next_bi[n] = n; for(int i = n-1; i>=0; i--){ if(v[i].type) next_bi[i] = i; else next_bi[i] = next_bi[i+1]; } pref[0] = 0; foru(i, n) pref[i+1] = pref[i] + v[i].plus; pref_linear[0] = linear(1, 0); foru(i, n) pref_linear[i+1] = pref_linear[i] + v[i].a; foru(_i, q){ ll x; int l, r; cin >> x >> l >> r; cout << querry(x, l, r) << endl; } } int main() { cin.tie(0); cout.tie(0); ios_base::sync_with_stdio(0); srand(time(NULL)); solve(); return 0; } |
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