#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pb push_back
#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define all(x) (x).begin(), (x).end()
#define BOOST ios_base::sync_with_stdio(0), cin.tie(0)
typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef vector<int> vi;
const int MOD = 1e9 + 7;
int bin_pow(int x, int n) {
if (n == 0)
return 1;
if (n % 2)
return (1LL * bin_pow(x, n - 1) * x) % MOD;
int half = bin_pow(x, n / 2);
return (1LL * half * half) % MOD;
}
void add(int &x, int y) {
x = (1LL * x + y + MOD) % MOD;
}
int radd(int x, int y) {
return (1LL * x + y + MOD) % MOD;
}
void mul(int &x, int y) {
x = (1LL * x * y) % MOD;
}
int rmul(int x, int y) {
return (1LL * x * y) % MOD;
}
const int MAXN = 5e5 + 5;
int a[MAXN], b[MAXN], prefa[MAXN],
prefb[MAXN], prefbinv[MAXN], biga[MAXN],
nxt[MAXN], sumsuf[MAXN], prv[MAXN];
void test_case() {
int n, q;
cin >> n >> q;
// vector<int> a(n), b(n);
memset(prefb, 1, sizeof(b)), memset(prefbinv, 1, sizeof(prefa));
memset(nxt, -1, sizeof(nxt)), memset(prv, -1, sizeof(nxt));
for (int i = 0; i < n; i++) {
cin >> a[i] >> b[i];
}
vector<int> prefa(n + 1, 0), prefb(n + 1, 1), prefbinv(n + 1, 1);
for (int i = 1; i <= n; i++) {
prefa[i] = radd(prefa[i - 1], a[i - 1]);
prefb[i] = rmul(prefb[i - 1], b[i - 1]);
prefbinv[i] = bin_pow(prefb[i], MOD - 2);
}
auto get_a = [&](int l, int r) {
int ans = prefa[r + 1] + MOD - prefa[l];
if (ans >= MOD)
ans -= MOD;
return ans;
};
auto get_b = [&](int l, int r) {
return rmul(prefb[r + 1], prefbinv[l]);
};
// vector<int> biga(n, 0);
for (ll l = 0, r = 0, cur_sum = 0; l < n; cur_sum -= a[l++]) {
while (r < n && cur_sum < MOD) {
cur_sum += a[r++];
}
biga[l] = (int)r;
}
// vector<int> nxt(n, -1), sumsuf(n, 0);
nxt[n - 1] = n, sumsuf[n - 1] = (b[n - 1] == 1 ? a[n - 1] : 0);
for (int i = n - 2; i >= 0; i--) {
nxt[i] = (b[i] == 1 ^ b[i + 1] == 1 ? i + 1 : nxt[i + 1]);
sumsuf[i] = sumsuf[i + 1];
if (b[i] == 1) {
add(sumsuf[i], rmul(a[i], get_b(i, n - 1)));
}
}
// vector<int> prv(n, -1);
prv[0] = -1;
for (int i = 1; i < n; i++) {
if (b[i - 1] == 1 ^ b[i] == 1) {
prv[i] = prv[i - 1];
} else {
prv[i] = i - 1;
}
}
while (q--) {
ll x;
int l, r;
cin >> x >> l >> r;
r--;
bool big = false;
int i = l;
while (i <= r && !big) {
if (b[i] == 1) {
int new_i = min(nxt[i], r + 1);
x += get_a(i, new_i - 1);
big |= x >= MOD || biga[i] <= new_i - 1;
x %= MOD;
i = new_i;
} else {
if (x + a[i] >= 1LL * x * b[i]) {
x += a[i];
} else {
x = 1LL * x * b[i];
}
big |= x >= MOD;
x %= MOD;
i++;
}
}
if (i > r) {
cout << x << "\n";
continue;
}
int rest = sumsuf[i];
if (r < n - 1) {
rest = radd(sumsuf[i], -sumsuf[r + 1]);
mul(rest, bin_pow(get_b(r + 1, n - 1), MOD - 2));
}
x = rmul((int)x, get_b(i, r));
x = radd(x, rest);
cout << x << "\n";
}
}
int32_t main() {
BOOST;
int q = 1;
// cin >> q;
while (q--) {
test_case();
}
}
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 | #include <bits/stdc++.h> using namespace std; #define fi first #define se second #define pb push_back #define rep(i, a, b) for (int i = a; i < (b); ++i) #define all(x) (x).begin(), (x).end() #define BOOST ios_base::sync_with_stdio(0), cin.tie(0) typedef long long ll; typedef long double ld; typedef pair<int, int> ii; typedef vector<int> vi; const int MOD = 1e9 + 7; int bin_pow(int x, int n) { if (n == 0) return 1; if (n % 2) return (1LL * bin_pow(x, n - 1) * x) % MOD; int half = bin_pow(x, n / 2); return (1LL * half * half) % MOD; } void add(int &x, int y) { x = (1LL * x + y + MOD) % MOD; } int radd(int x, int y) { return (1LL * x + y + MOD) % MOD; } void mul(int &x, int y) { x = (1LL * x * y) % MOD; } int rmul(int x, int y) { return (1LL * x * y) % MOD; } const int MAXN = 5e5 + 5; int a[MAXN], b[MAXN], prefa[MAXN], prefb[MAXN], prefbinv[MAXN], biga[MAXN], nxt[MAXN], sumsuf[MAXN], prv[MAXN]; void test_case() { int n, q; cin >> n >> q; // vector<int> a(n), b(n); memset(prefb, 1, sizeof(b)), memset(prefbinv, 1, sizeof(prefa)); memset(nxt, -1, sizeof(nxt)), memset(prv, -1, sizeof(nxt)); for (int i = 0; i < n; i++) { cin >> a[i] >> b[i]; } vector<int> prefa(n + 1, 0), prefb(n + 1, 1), prefbinv(n + 1, 1); for (int i = 1; i <= n; i++) { prefa[i] = radd(prefa[i - 1], a[i - 1]); prefb[i] = rmul(prefb[i - 1], b[i - 1]); prefbinv[i] = bin_pow(prefb[i], MOD - 2); } auto get_a = [&](int l, int r) { int ans = prefa[r + 1] + MOD - prefa[l]; if (ans >= MOD) ans -= MOD; return ans; }; auto get_b = [&](int l, int r) { return rmul(prefb[r + 1], prefbinv[l]); }; // vector<int> biga(n, 0); for (ll l = 0, r = 0, cur_sum = 0; l < n; cur_sum -= a[l++]) { while (r < n && cur_sum < MOD) { cur_sum += a[r++]; } biga[l] = (int)r; } // vector<int> nxt(n, -1), sumsuf(n, 0); nxt[n - 1] = n, sumsuf[n - 1] = (b[n - 1] == 1 ? a[n - 1] : 0); for (int i = n - 2; i >= 0; i--) { nxt[i] = (b[i] == 1 ^ b[i + 1] == 1 ? i + 1 : nxt[i + 1]); sumsuf[i] = sumsuf[i + 1]; if (b[i] == 1) { add(sumsuf[i], rmul(a[i], get_b(i, n - 1))); } } // vector<int> prv(n, -1); prv[0] = -1; for (int i = 1; i < n; i++) { if (b[i - 1] == 1 ^ b[i] == 1) { prv[i] = prv[i - 1]; } else { prv[i] = i - 1; } } while (q--) { ll x; int l, r; cin >> x >> l >> r; r--; bool big = false; int i = l; while (i <= r && !big) { if (b[i] == 1) { int new_i = min(nxt[i], r + 1); x += get_a(i, new_i - 1); big |= x >= MOD || biga[i] <= new_i - 1; x %= MOD; i = new_i; } else { if (x + a[i] >= 1LL * x * b[i]) { x += a[i]; } else { x = 1LL * x * b[i]; } big |= x >= MOD; x %= MOD; i++; } } if (i > r) { cout << x << "\n"; continue; } int rest = sumsuf[i]; if (r < n - 1) { rest = radd(sumsuf[i], -sumsuf[r + 1]); mul(rest, bin_pow(get_b(r + 1, n - 1), MOD - 2)); } x = rmul((int)x, get_b(i, r)); x = radd(x, rest); cout << x << "\n"; } } int32_t main() { BOOST; int q = 1; // cin >> q; while (q--) { test_case(); } } |
English