#include<bits/stdc++.h>
using namespace std;
#define int int64_t
const int64_t mod = 1e9+7;
const int maxn = 1e6+10;
int inf;
double infd;
int64_t mpowm(int64_t x, int64_t w)
{
if (w == 0) return 1;
if (w % 2 == 1)
{
return (mpowm(x, w-1)*x) % mod;
}
else
{
int64_t a = mpowm(x, w/2);
return (a*a)%mod;
}
}
int64_t inv_mod(int64_t x)
{
return mpowm(x, mod-2);
}
int64_t silm(int64_t x)
{
int64_t ans = 1;
for (int64_t i = 1; i <= x; i++)
{
ans *= i;
ans %= mod;
}
return ans;
}
int64_t sil[maxn];
void calc_sil()
{
sil[0] = 1;
for (int i = 1; i < maxn; i++)
{
sil[i] = (sil[i-1] * i) % mod;
}
}
int64_t sym_new(int64_t n, int64_t k)
{
int64_t ans = silm(n);
ans *= inv_mod(silm(k));
ans %= mod;
ans *= inv_mod(silm(n-k));
ans %= mod;
return ans;
}
/*
*/
int n, q;
int a[maxn];
int b[maxn];
double eqlx[maxn]; // equlibrium x, x + a = x * b
double sm_ex[maxn]; // suffix maximum of eqlx
int ps_a[maxn]; // prefix sum of a
int sp_b[maxn]; // sufix product of b
int next_b[maxn]; // index of next b[i] >= 2
int sswa[maxn]; // suffix sum of weighted by sp_b of a[i] where b[i] == 1
int calc_psa(int l, int r)
{
int val = ps_a[r] - ps_a[l-1];
val %= mod;
if (val < 0)
{
val += mod;
}
return val;
}
int calc_spb(int l, int r)
{
if (l > r)
{
return 1;
}
int val = ( sp_b[l] * inv_mod(sp_b[r+1]) ) % mod;
return val;
}
void build_ds()
{
for (int i = 1; i <= n; i++)
{
if (b[i] == 1)
{
eqlx[i] = infd;
continue;
}
eqlx[i] = a[i] / (b[i] - 1);
}
sm_ex[n+1] = 0;
sp_b[n+1] = 1;
next_b[n+1] = n+1;
sswa[n+1] = 0;
for (int i = n; i >= 0; i--)
{
sm_ex[i] = max(eqlx[i], sm_ex[i+1]);
sp_b[i] = (sp_b[i+1] * b[i]) % mod;
next_b[i] = next_b[i+1];
if (b[i] >= 2)
{
next_b[i] = i;
}
sswa[i] += sswa[i+1];
if (b[i] == 1)
{
sswa[i] += (a[i] * sp_b[i+1]) % mod;
sswa[i] %= mod;
}
}
ps_a[0] = 0;
for (int i = 1; i <= n+1; i++)
{
ps_a[i] = (a[i] + ps_a[i-1]) % mod;
}
/*cout << "show_ds" << endl;
for (int i = 1; i <= n; i++)
{
cout << "i=" << i << " ps_a=" << ps_a[i] << " eqlx[i]=" << eqlx[i] << " sm_ex[i]=" << sm_ex[i] << " sp_b[i]=" << sp_b[i] << " next_b[i]=" << next_b[i] << " sswa[i]=" << sswa[i] << endl;
}*/
}
int answer_query(int x, int l, int r)
{
//cout << "answer_query x=" << x << " l=" << l << " r=" << r << endl;
l++;
int cx = x;
double cxd = x;
int i = l;
while (i <= r && cxd <= sm_ex[i])
{
if (cxd >= eqlx[i] && b[i] > 1)
{
//cout << "i=" << i << " mult " << b[i] << endl;
cx *= b[i];
cx %= mod;
cxd *= b[i];
i++;
}
else
{
int ni = max(min(next_b[i]-1, r), i);
//cout << "i=" << i << " add " << calc_psa(i, ni) << " ni=" << ni << endl;
cx += calc_psa(i, ni);
cx %= mod;
cxd += calc_psa(i, ni);
i = ni+1;
}
}
//cout << "i=" << i << endl;
if (i <= r)
{
cx *= calc_spb(i, r);
cx %= mod;
cx += (sswa[i] - sswa[r+1]) * inv_mod(calc_spb(r+1, n));
//cout << "endby mult=" << calc_spb(i, r) << " add=" << sswa[i] * inv_mod(calc_spb(r+1, n)) << endl;
}
//cout << "ans=" << cx << endl;
return cx;
}
void tc()
{
cin >> n >> q;
for (int i = 1; i <= n; i++)
{
cin >> a[i] >> b[i];
}
build_ds();
while (q--)
{
int x, l, r;
cin >> x >> l >> r;
cout << answer_query(x, l, r) << endl;
}
}
int32_t main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
inf = numeric_limits<int>::max()/2;
infd = numeric_limits<double>::max()/2;
int T = 1;
//cin >> T;
while (T--) tc();
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 | #include<bits/stdc++.h> using namespace std; #define int int64_t const int64_t mod = 1e9+7; const int maxn = 1e6+10; int inf; double infd; int64_t mpowm(int64_t x, int64_t w) { if (w == 0) return 1; if (w % 2 == 1) { return (mpowm(x, w-1)*x) % mod; } else { int64_t a = mpowm(x, w/2); return (a*a)%mod; } } int64_t inv_mod(int64_t x) { return mpowm(x, mod-2); } int64_t silm(int64_t x) { int64_t ans = 1; for (int64_t i = 1; i <= x; i++) { ans *= i; ans %= mod; } return ans; } int64_t sil[maxn]; void calc_sil() { sil[0] = 1; for (int i = 1; i < maxn; i++) { sil[i] = (sil[i-1] * i) % mod; } } int64_t sym_new(int64_t n, int64_t k) { int64_t ans = silm(n); ans *= inv_mod(silm(k)); ans %= mod; ans *= inv_mod(silm(n-k)); ans %= mod; return ans; } /* */ int n, q; int a[maxn]; int b[maxn]; double eqlx[maxn]; // equlibrium x, x + a = x * b double sm_ex[maxn]; // suffix maximum of eqlx int ps_a[maxn]; // prefix sum of a int sp_b[maxn]; // sufix product of b int next_b[maxn]; // index of next b[i] >= 2 int sswa[maxn]; // suffix sum of weighted by sp_b of a[i] where b[i] == 1 int calc_psa(int l, int r) { int val = ps_a[r] - ps_a[l-1]; val %= mod; if (val < 0) { val += mod; } return val; } int calc_spb(int l, int r) { if (l > r) { return 1; } int val = ( sp_b[l] * inv_mod(sp_b[r+1]) ) % mod; return val; } void build_ds() { for (int i = 1; i <= n; i++) { if (b[i] == 1) { eqlx[i] = infd; continue; } eqlx[i] = a[i] / (b[i] - 1); } sm_ex[n+1] = 0; sp_b[n+1] = 1; next_b[n+1] = n+1; sswa[n+1] = 0; for (int i = n; i >= 0; i--) { sm_ex[i] = max(eqlx[i], sm_ex[i+1]); sp_b[i] = (sp_b[i+1] * b[i]) % mod; next_b[i] = next_b[i+1]; if (b[i] >= 2) { next_b[i] = i; } sswa[i] += sswa[i+1]; if (b[i] == 1) { sswa[i] += (a[i] * sp_b[i+1]) % mod; sswa[i] %= mod; } } ps_a[0] = 0; for (int i = 1; i <= n+1; i++) { ps_a[i] = (a[i] + ps_a[i-1]) % mod; } /*cout << "show_ds" << endl; for (int i = 1; i <= n; i++) { cout << "i=" << i << " ps_a=" << ps_a[i] << " eqlx[i]=" << eqlx[i] << " sm_ex[i]=" << sm_ex[i] << " sp_b[i]=" << sp_b[i] << " next_b[i]=" << next_b[i] << " sswa[i]=" << sswa[i] << endl; }*/ } int answer_query(int x, int l, int r) { //cout << "answer_query x=" << x << " l=" << l << " r=" << r << endl; l++; int cx = x; double cxd = x; int i = l; while (i <= r && cxd <= sm_ex[i]) { if (cxd >= eqlx[i] && b[i] > 1) { //cout << "i=" << i << " mult " << b[i] << endl; cx *= b[i]; cx %= mod; cxd *= b[i]; i++; } else { int ni = max(min(next_b[i]-1, r), i); //cout << "i=" << i << " add " << calc_psa(i, ni) << " ni=" << ni << endl; cx += calc_psa(i, ni); cx %= mod; cxd += calc_psa(i, ni); i = ni+1; } } //cout << "i=" << i << endl; if (i <= r) { cx *= calc_spb(i, r); cx %= mod; cx += (sswa[i] - sswa[r+1]) * inv_mod(calc_spb(r+1, n)); //cout << "endby mult=" << calc_spb(i, r) << " add=" << sswa[i] * inv_mod(calc_spb(r+1, n)) << endl; } //cout << "ans=" << cx << endl; return cx; } void tc() { cin >> n >> q; for (int i = 1; i <= n; i++) { cin >> a[i] >> b[i]; } build_ds(); while (q--) { int x, l, r; cin >> x >> l >> r; cout << answer_query(x, l, r) << endl; } } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(0); inf = numeric_limits<int>::max()/2; infd = numeric_limits<double>::max()/2; int T = 1; //cin >> T; while (T--) tc(); return 0; } |
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