#include <bits/stdc++.h>
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())
using namespace std;
#ifdef LOCAL
template<typename A, typename B>
auto&operator<<(auto&o,pair<A, B>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<&","[!i++]<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif
using i64 = long long;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<i64, i64>;
using vi = vector<int>;
using vll = vector<i64>;
const int MOD = 1000 * 1000 * 1000 + 7;
inline void add_mod(ll &a, ll b) {
a += b;
if (a >= MOD) {
a -= MOD;
}
}
inline ll mul_mod(ll a, ll b) {
return (a * b) % MOD;
}
struct LinFuncTree {
struct Node {
ll a, b; // x -> ax+b (mod MOD)
Node() : a{1}, b{0} {}
Node(ll a_, ll b_) : a{a_}, b{b_} {}
Node Merge(const Node &rhs) const {
// order: *this; rhs
// x -> rhs.a * (ax + b) + rhs.b
const ll ret_a = mul_mod(rhs.a, a);
ll ret_b = mul_mod(rhs.a, b);
add_mod(ret_b, rhs.b);
return Node(ret_a, ret_b);
}
};
vector<Node> nodes;
int base;
LinFuncTree(int n) : base{1} {
while (base < n + 2) { base *= 2; }
nodes.resize(base * 2);
}
void Set(int pos, ll a, ll b) {
pos += base;
nodes[pos] = Node(a, b);
pos /= 2;
while (pos) {
nodes[pos] = nodes[pos * 2].Merge(nodes[pos * 2 + 1]);
pos /= 2;
}
}
Node ComposeInternal(ll L, ll R) const {
if (L > R) {
return Node{};
}
L += base; R += base;
if (L == R) {
return nodes[L];
}
Node res_l = nodes[L], res_r = nodes[R];
while (L / 2 != R / 2) {
if (L % 2 == 0) {
res_l = res_l.Merge(nodes[L + 1]);
}
if (R % 2 == 1) {
res_r = nodes[R - 1].Merge(res_r);
}
L /= 2;
R /= 2;
}
return res_l.Merge(res_r);
}
pll Compose(ll L, ll R) const {
const Node ans = ComposeInternal(L, R);
return {ans.a, ans.b};
}
};
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout << fixed << setprecision(14);
cerr << fixed << setprecision(6);
int n, q;
cin >> n >> q;
vll A(n), B(n);
vll pref_A(n + 1);
for (int i = 0; i < n; ++i) {
cin >> A[i] >> B[i];
pref_A[i + 1] = pref_A[i] + A[i];
}
const ll max_A = *max_element(ALL(A));
vi where_next_B(n + 1);
where_next_B[n] = n;
for (int i = n - 1; i >= 0; --i) {
if (B[i] >= 2) {
where_next_B[i] = i;
} else {
where_next_B[i] = where_next_B[i + 1];
}
}
LinFuncTree lin_tree(n);
for (int i = 0; i < n; ++i) {
ll mul_by, inc_by;
if (B[i] == 1) {
mul_by = 1;
inc_by = A[i];
} else {
mul_by = B[i];
inc_by = 0;
}
lin_tree.Set(i, mul_by, inc_by);
}
auto SolveQuery = [&](int L, int R, ll x) {
debug("start", L, R, x);
while (L < R && x < max_A) {
if (B[L] >= 2) {
x = max(x + A[L], x * B[L]);
++L;
} else {
const int skip_to = min(R, where_next_B[L]);
assert(skip_to > L);
x += (pref_A[skip_to] - pref_A[L]);
L = skip_to;
}
debug(L, R, x);
}
x %= MOD;
const auto [comp_mul, comp_inc] = lin_tree.Compose(L, R - 1);
debug(comp_mul, comp_inc);
x = mul_mod(x, comp_mul);
add_mod(x, comp_inc);
return x;
};
for (int qid = 0; qid < q; ++qid) {
int L, R, x;
cin >> x >> L >> R;
cout << SolveQuery(L, R, x) << "\n";
}
}
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 | #include <bits/stdc++.h> #define ALL(x) (x).begin(), (x).end() #define SZ(x) ((int)(x).size()) using namespace std; #ifdef LOCAL template<typename A, typename B> auto&operator<<(auto&o,pair<A, B>p){return o<<"("<<p.first<<", "<<p.second<<")";} auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<&","[!i++]<<e;return o<<"}";} #define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X) #else #define debug(...){} #endif using i64 = long long; using ll = long long; using pii = pair<int, int>; using pll = pair<i64, i64>; using vi = vector<int>; using vll = vector<i64>; const int MOD = 1000 * 1000 * 1000 + 7; inline void add_mod(ll &a, ll b) { a += b; if (a >= MOD) { a -= MOD; } } inline ll mul_mod(ll a, ll b) { return (a * b) % MOD; } struct LinFuncTree { struct Node { ll a, b; // x -> ax+b (mod MOD) Node() : a{1}, b{0} {} Node(ll a_, ll b_) : a{a_}, b{b_} {} Node Merge(const Node &rhs) const { // order: *this; rhs // x -> rhs.a * (ax + b) + rhs.b const ll ret_a = mul_mod(rhs.a, a); ll ret_b = mul_mod(rhs.a, b); add_mod(ret_b, rhs.b); return Node(ret_a, ret_b); } }; vector<Node> nodes; int base; LinFuncTree(int n) : base{1} { while (base < n + 2) { base *= 2; } nodes.resize(base * 2); } void Set(int pos, ll a, ll b) { pos += base; nodes[pos] = Node(a, b); pos /= 2; while (pos) { nodes[pos] = nodes[pos * 2].Merge(nodes[pos * 2 + 1]); pos /= 2; } } Node ComposeInternal(ll L, ll R) const { if (L > R) { return Node{}; } L += base; R += base; if (L == R) { return nodes[L]; } Node res_l = nodes[L], res_r = nodes[R]; while (L / 2 != R / 2) { if (L % 2 == 0) { res_l = res_l.Merge(nodes[L + 1]); } if (R % 2 == 1) { res_r = nodes[R - 1].Merge(res_r); } L /= 2; R /= 2; } return res_l.Merge(res_r); } pll Compose(ll L, ll R) const { const Node ans = ComposeInternal(L, R); return {ans.a, ans.b}; } }; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout << fixed << setprecision(14); cerr << fixed << setprecision(6); int n, q; cin >> n >> q; vll A(n), B(n); vll pref_A(n + 1); for (int i = 0; i < n; ++i) { cin >> A[i] >> B[i]; pref_A[i + 1] = pref_A[i] + A[i]; } const ll max_A = *max_element(ALL(A)); vi where_next_B(n + 1); where_next_B[n] = n; for (int i = n - 1; i >= 0; --i) { if (B[i] >= 2) { where_next_B[i] = i; } else { where_next_B[i] = where_next_B[i + 1]; } } LinFuncTree lin_tree(n); for (int i = 0; i < n; ++i) { ll mul_by, inc_by; if (B[i] == 1) { mul_by = 1; inc_by = A[i]; } else { mul_by = B[i]; inc_by = 0; } lin_tree.Set(i, mul_by, inc_by); } auto SolveQuery = [&](int L, int R, ll x) { debug("start", L, R, x); while (L < R && x < max_A) { if (B[L] >= 2) { x = max(x + A[L], x * B[L]); ++L; } else { const int skip_to = min(R, where_next_B[L]); assert(skip_to > L); x += (pref_A[skip_to] - pref_A[L]); L = skip_to; } debug(L, R, x); } x %= MOD; const auto [comp_mul, comp_inc] = lin_tree.Compose(L, R - 1); debug(comp_mul, comp_inc); x = mul_mod(x, comp_mul); add_mod(x, comp_inc); return x; }; for (int qid = 0; qid < q; ++qid) { int L, R, x; cin >> x >> L >> R; cout << SolveQuery(L, R, x) << "\n"; } } |
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