#include <bits/stdc++.h>
using namespace std;
#define fwd(i, a, n) for (int i = (a); i < (n); i++)
#define rep(i, n) fwd(i, 0, n)
#define all(X) X.begin(), X.end()
#define sz(X) int(size(X))
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
using pii = pair<int, int>; using vi = vector<int>;
using ll = long long; using ld = long double;
#ifdef LOC
auto SS = signal(6, [](int) { *(int *)0 = 0; });
#define DTP(x, y) auto operator<<(auto &o, auto a) -> decltype(y, o) { o << "("; x; return o << ")"; }
auto operator<<(auto &o, auto a) -> decltype(all(a), o);
DTP(o << a.fi << ", " << a.se, a.se);
DTP(for (auto i : a) o << i << ", ", all(a));
#define deb(x...) cerr << setw(4) << __LINE__ << ":[" #x "]: ", [](auto... arg_) { (( cerr << arg_ << ", " ), ...) << '\n'; }(x)
#else
#define deb(...) 0
#endif
const int P = 1e9 + 7, phiP = P - 1;
struct mint {
int x = 0;
mint operator+(mint o) const {return {x + o.x >= P ? x + o.x - P : x + o.x}; }
mint operator-(mint o) const {return {x < o.x ? x - o.x + P : x - o.x}; }
mint operator+() const {return *this; }
mint operator-() const {return {x ? P - x : 0}; }
mint operator*(mint o) const {return {int(ll(x) * o.x % P)}; }
mint operator/(mint o) const {return *this * o.inv(); }
mint & operator+=(mint o) {return *this = *this + o; }
mint & operator-=(mint o) {return *this = *this - o; }
mint & operator*=(mint o) {return *this = *this * o; }
mint & operator/=(mint o) {return *this = *this / o; }
mint pow(ll e) const {
mint ret{1}, b(*this);
for (; e; e >>= 1) {
if (e & 1)
ret *= b;
b *= b;
}
return ret;
}
mint inv() const {return pow(phiP - 1); }
};
auto &operator<<(auto &os, mint m) {
return os << m.x - (2 * m.x >= P && &os == &cerr ? P : 0);
}
using func = pair<mint, mint>; // ax + b
func operator*(const func &s, const func &t) {
return {
s.fi * t.fi,
s.se + s.fi * t.se
};
}
func inv(const func &s) {
mint a = s.fi.inv();
mint b = -a * s.se;
func f{a, b};
{
func g = f * s;
assert(g.fi.x == 1);
assert(g.se.x == 0);
}
return f;
}
void solve() {
int n, q;
cin >> n >> q;
vi a(n), b(n); // add, mul
vector<ll> prefA(n);
vector<func> prefB(n);
vi nxt2(n);
rep(i, n) {
cin >> a[i] >> b[i];
prefA[i] = a[i];
prefB[i].fi.x = b[i] == 1 ? 1 : b[i];
prefB[i].se.x = b[i] == 1 ? a[i] : 0;
if (i) {
prefA[i] += prefA[i-1];
prefB[i] = prefB[i] * prefB[i-1];
}
}
for (int i = n-1; i >= 0; --i) {
if (i == n-1)
nxt2[i] = n;
else
nxt2[i] = nxt2[i+1];
if (b[i] != 1)
nxt2[i] = i;
}
auto sum = [&](int l, int r) -> ll {
return prefA[r] - (l ? prefA[l-1] : 0);
};
auto prod = [&](int l, int r) -> func {
return prefB[r] * (l ? inv(prefB[l-1]) : func(mint{1}, mint{0}));
};
// deb(prefA);
// deb(prefB);
rep(_, q) {
ll x;
int l, r;
cin >> x >> l >> r;
--r;
while (l <= r) {
// deb(x, l, r);
if (x >= P) {
// deb("skip", l, r);
auto [A, B] = prod(l, r);
x = x % P * A.x + B.x;
break;
}
if (b[l] > 1) {
x = max(x + a[l], x * b[l]);
++l;
continue;
}
int R = min(r, nxt2[l] - 1);
x += sum(l, R);
l = R + 1;
}
x %= P;
cout << x << '\n';
}
}
int32_t main() {
cin.tie(0)->sync_with_stdio(0);
cout << fixed << setprecision(10);
int z = 1;
// cin >> z;
rep(_, z) solve();
cout << flush;
_Exit(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 | #include <bits/stdc++.h> using namespace std; #define fwd(i, a, n) for (int i = (a); i < (n); i++) #define rep(i, n) fwd(i, 0, n) #define all(X) X.begin(), X.end() #define sz(X) int(size(X)) #define pb push_back #define eb emplace_back #define fi first #define se second using pii = pair<int, int>; using vi = vector<int>; using ll = long long; using ld = long double; #ifdef LOC auto SS = signal(6, [](int) { *(int *)0 = 0; }); #define DTP(x, y) auto operator<<(auto &o, auto a) -> decltype(y, o) { o << "("; x; return o << ")"; } auto operator<<(auto &o, auto a) -> decltype(all(a), o); DTP(o << a.fi << ", " << a.se, a.se); DTP(for (auto i : a) o << i << ", ", all(a)); #define deb(x...) cerr << setw(4) << __LINE__ << ":[" #x "]: ", [](auto... arg_) { (( cerr << arg_ << ", " ), ...) << '\n'; }(x) #else #define deb(...) 0 #endif const int P = 1e9 + 7, phiP = P - 1; struct mint { int x = 0; mint operator+(mint o) const {return {x + o.x >= P ? x + o.x - P : x + o.x}; } mint operator-(mint o) const {return {x < o.x ? x - o.x + P : x - o.x}; } mint operator+() const {return *this; } mint operator-() const {return {x ? P - x : 0}; } mint operator*(mint o) const {return {int(ll(x) * o.x % P)}; } mint operator/(mint o) const {return *this * o.inv(); } mint & operator+=(mint o) {return *this = *this + o; } mint & operator-=(mint o) {return *this = *this - o; } mint & operator*=(mint o) {return *this = *this * o; } mint & operator/=(mint o) {return *this = *this / o; } mint pow(ll e) const { mint ret{1}, b(*this); for (; e; e >>= 1) { if (e & 1) ret *= b; b *= b; } return ret; } mint inv() const {return pow(phiP - 1); } }; auto &operator<<(auto &os, mint m) { return os << m.x - (2 * m.x >= P && &os == &cerr ? P : 0); } using func = pair<mint, mint>; // ax + b func operator*(const func &s, const func &t) { return { s.fi * t.fi, s.se + s.fi * t.se }; } func inv(const func &s) { mint a = s.fi.inv(); mint b = -a * s.se; func f{a, b}; { func g = f * s; assert(g.fi.x == 1); assert(g.se.x == 0); } return f; } void solve() { int n, q; cin >> n >> q; vi a(n), b(n); // add, mul vector<ll> prefA(n); vector<func> prefB(n); vi nxt2(n); rep(i, n) { cin >> a[i] >> b[i]; prefA[i] = a[i]; prefB[i].fi.x = b[i] == 1 ? 1 : b[i]; prefB[i].se.x = b[i] == 1 ? a[i] : 0; if (i) { prefA[i] += prefA[i-1]; prefB[i] = prefB[i] * prefB[i-1]; } } for (int i = n-1; i >= 0; --i) { if (i == n-1) nxt2[i] = n; else nxt2[i] = nxt2[i+1]; if (b[i] != 1) nxt2[i] = i; } auto sum = [&](int l, int r) -> ll { return prefA[r] - (l ? prefA[l-1] : 0); }; auto prod = [&](int l, int r) -> func { return prefB[r] * (l ? inv(prefB[l-1]) : func(mint{1}, mint{0})); }; // deb(prefA); // deb(prefB); rep(_, q) { ll x; int l, r; cin >> x >> l >> r; --r; while (l <= r) { // deb(x, l, r); if (x >= P) { // deb("skip", l, r); auto [A, B] = prod(l, r); x = x % P * A.x + B.x; break; } if (b[l] > 1) { x = max(x + a[l], x * b[l]); ++l; continue; } int R = min(r, nxt2[l] - 1); x += sum(l, R); l = R + 1; } x %= P; cout << x << '\n'; } } int32_t main() { cin.tie(0)->sync_with_stdio(0); cout << fixed << setprecision(10); int z = 1; // cin >> z; rep(_, z) solve(); cout << flush; _Exit(0); } |
English