#include <bits/stdc++.h>
#define all(x) (x).begin(), (x).end()
using namespace std;
#ifdef LOCAL
#include "debug.h"
#else
struct debug {
template <class c>
debug& operator<<(const c&) { return *this; }
};
#define imie(...) ""
#endif
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
int R(int a, int b) {
static mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
return uniform_int_distribution<int>(a, b)(rng);
}
constexpr int ALPHA = 26, MAXN = 500'005, MOD = 1'000'000'007;
constexpr int INF = MOD;
int a[MAXN], b[MAXN], g[MAXN], blok_sum[MAXN];
ll pref_a[MAXN];
ll suma(int l, int r) {
return pref_a[r] - pref_a[l - 1];
}
// Trzyma wartości (a * x + b).
pii tree[4 * MAXN];
pii sklej(pii a, pii b) {
auto [al, bl] = a;
auto [ar, br] = b;
// Podstawiam t = al * x + bl w rownanie z prawego poddrzewa.
// ar * t + br = ar * (al * x + bl) + br = ar * al * x + ar * bl + br.
// Czyli para której szukam to (ar * al, ar * bl + br).
return {1LL * ar * al % MOD, (1LL * ar * bl + br) % MOD};
}
void build(int pos, int l, int r) {
if (l == r) {
if (b[r] == 1) tree[pos] = {1, a[r]};
else tree[pos] = {b[r], 0};
debug() << imie(pos) << imie(l) << imie(r) << imie(tree[pos]);
return;
}
int m = (l + r) / 2;
build(pos*2, l, m);
build(pos*2+1, m+1, r);
tree[pos] = sklej(tree[pos*2], tree[pos*2+1]);
debug() << imie(pos) << imie(l) << imie(r) << imie(tree[pos]);
}
int ql, qr;
pii wynik;
void query(int pos, int l, int r) {
if (l > qr || r < ql) return;
if (l >= ql && r <= qr) {
wynik = sklej(wynik, tree[pos]);
return;
}
int m = (l + r) / 2;
query(pos*2, l, m);
query(pos*2+1, m+1, r);
}
void solve(int tc) {
int n, q;
cin >> n >> q;
for (int i = 1; i <= n; i++) {
cin >> a[i] >> b[i];
pref_a[i] = pref_a[i - 1] + a[i];
if (b[i] == 1) g[i] = INF;
else {
g[i] = (-a[i]) / (1 - b[i]) + 1;
}
}
blok_sum[n] = n;
for (int i = n; i > 1; i--) {
if (g[i - 1] - 1 + a[i - 1] < g[i]) {
blok_sum[i-1] = blok_sum[i];
} else {
blok_sum[i-1] = i-1;
}
}
build(1, 1, n);
for (int i = 1; i <= n; i++) {
debug() << imie(i) << imie(g[i]) << imie(blok_sum[i]);
}
while (q--) {
ll x;
int l, r;
cin >> x >> l >> r;
bool przebilem_mod = false;
for (int i = l + 1; i <= r; i++) {
if (przebilem_mod) {
ql = i;
qr = r;
wynik = {1, 0};
query(1, 1, n);
debug() << imie(ql) << imie(qr) << imie(wynik);
x = (x * wynik.first + wynik.second) % MOD;
break;
} else {
if (x >= g[i]) {
x = x * b[i];
} else {
int koniec = min(r, blok_sum[i]);
debug() << imie(koniec);
x += suma(i, koniec);
i = koniec;
}
if (x > MOD) {
przebilem_mod = true;
x %= MOD;
}
}
debug() << imie(i) << imie(x) << imie(przebilem_mod);
}
cout << x << "\n";
}
}
int32_t main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int tests = 1;
debug() << imie(tests);
for (int tc = 1; tc <= tests; tc++) {
solve(tc);
}
}
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 | #include <bits/stdc++.h> #define all(x) (x).begin(), (x).end() using namespace std; #ifdef LOCAL #include "debug.h" #else struct debug { template <class c> debug& operator<<(const c&) { return *this; } }; #define imie(...) "" #endif using ll = long long; using ld = long double; using pii = pair<int, int>; int R(int a, int b) { static mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); return uniform_int_distribution<int>(a, b)(rng); } constexpr int ALPHA = 26, MAXN = 500'005, MOD = 1'000'000'007; constexpr int INF = MOD; int a[MAXN], b[MAXN], g[MAXN], blok_sum[MAXN]; ll pref_a[MAXN]; ll suma(int l, int r) { return pref_a[r] - pref_a[l - 1]; } // Trzyma wartości (a * x + b). pii tree[4 * MAXN]; pii sklej(pii a, pii b) { auto [al, bl] = a; auto [ar, br] = b; // Podstawiam t = al * x + bl w rownanie z prawego poddrzewa. // ar * t + br = ar * (al * x + bl) + br = ar * al * x + ar * bl + br. // Czyli para której szukam to (ar * al, ar * bl + br). return {1LL * ar * al % MOD, (1LL * ar * bl + br) % MOD}; } void build(int pos, int l, int r) { if (l == r) { if (b[r] == 1) tree[pos] = {1, a[r]}; else tree[pos] = {b[r], 0}; debug() << imie(pos) << imie(l) << imie(r) << imie(tree[pos]); return; } int m = (l + r) / 2; build(pos*2, l, m); build(pos*2+1, m+1, r); tree[pos] = sklej(tree[pos*2], tree[pos*2+1]); debug() << imie(pos) << imie(l) << imie(r) << imie(tree[pos]); } int ql, qr; pii wynik; void query(int pos, int l, int r) { if (l > qr || r < ql) return; if (l >= ql && r <= qr) { wynik = sklej(wynik, tree[pos]); return; } int m = (l + r) / 2; query(pos*2, l, m); query(pos*2+1, m+1, r); } void solve(int tc) { int n, q; cin >> n >> q; for (int i = 1; i <= n; i++) { cin >> a[i] >> b[i]; pref_a[i] = pref_a[i - 1] + a[i]; if (b[i] == 1) g[i] = INF; else { g[i] = (-a[i]) / (1 - b[i]) + 1; } } blok_sum[n] = n; for (int i = n; i > 1; i--) { if (g[i - 1] - 1 + a[i - 1] < g[i]) { blok_sum[i-1] = blok_sum[i]; } else { blok_sum[i-1] = i-1; } } build(1, 1, n); for (int i = 1; i <= n; i++) { debug() << imie(i) << imie(g[i]) << imie(blok_sum[i]); } while (q--) { ll x; int l, r; cin >> x >> l >> r; bool przebilem_mod = false; for (int i = l + 1; i <= r; i++) { if (przebilem_mod) { ql = i; qr = r; wynik = {1, 0}; query(1, 1, n); debug() << imie(ql) << imie(qr) << imie(wynik); x = (x * wynik.first + wynik.second) % MOD; break; } else { if (x >= g[i]) { x = x * b[i]; } else { int koniec = min(r, blok_sum[i]); debug() << imie(koniec); x += suma(i, koniec); i = koniec; } if (x > MOD) { przebilem_mod = true; x %= MOD; } } debug() << imie(i) << imie(x) << imie(przebilem_mod); } cout << x << "\n"; } } int32_t main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int tests = 1; debug() << imie(tests); for (int tc = 1; tc <= tests; tc++) { solve(tc); } } |
English