#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<ll, ll>;
constexpr int MAXN = 5e5+2;
constexpr ll MOD = 1e9+7;
pii eve[MAXN];
//cp-algorithms
struct SqrtTreeItem {
ll val{};
ll mul{1ll};
bool over{};
bool mover{};
};
SqrtTreeItem op(const SqrtTreeItem &a, const SqrtTreeItem &b) {
ll res = a.val*b.mul+b.val;
bool ov = (res >= MOD);
ov |= a.over;
ov |= b.over;
bool mov = ((a.mul*b.mul) >= MOD);
mov |= a.mover;
mov |= b.mover;
return SqrtTreeItem{res%MOD,(a.mul*b.mul)%MOD, ov, mov};
}
inline int log2Up(int n) {
int res = 0;
while ((1 << res) < n) {
res++;
}
return res;
}
class SqrtTree {
private:
int n, lg, indexSz;
vector<SqrtTreeItem> v;
vector<int> clz, layers, onLayer;
vector< vector<SqrtTreeItem> > pref, suf, between;
inline void buildBlock(int layer, int l, int r) {
pref[layer][l] = v[l];
for (int i = l+1; i < r; i++) {
pref[layer][i] = op(pref[layer][i-1], v[i]);
}
suf[layer][r-1] = v[r-1];
for (int i = r-2; i >= l; i--) {
suf[layer][i] = op(v[i], suf[layer][i+1]);
}
}
inline void buildBetween(int layer, int lBound, int rBound, int betweenOffs) {
int bSzLog = (layers[layer]+1) >> 1;
int bCntLog = layers[layer] >> 1;
int bSz = 1 << bSzLog;
int bCnt = (rBound - lBound + bSz - 1) >> bSzLog;
for (int i = 0; i < bCnt; i++) {
SqrtTreeItem ans;
for (int j = i; j < bCnt; j++) {
SqrtTreeItem add = suf[layer][lBound + (j << bSzLog)];
ans = (i == j) ? add : op(ans, add);
between[layer-1][betweenOffs + lBound + (i << bCntLog) + j] = ans;
}
}
}
inline void buildBetweenZero() {
int bSzLog = (lg+1) >> 1;
for (int i = 0; i < indexSz; i++) {
v[n+i] = suf[0][i << bSzLog];
}
build(1, n, n + indexSz, (1 << lg) - n);
}
inline void updateBetweenZero(int bid) {
int bSzLog = (lg+1) >> 1;
v[n+bid] = suf[0][bid << bSzLog];
update(1, n, n + indexSz, (1 << lg) - n, n+bid);
}
void build(int layer, int lBound, int rBound, int betweenOffs) {
if (layer >= (int)layers.size()) {
return;
}
int bSz = 1 << ((layers[layer]+1) >> 1);
for (int l = lBound; l < rBound; l += bSz) {
int r = min(l + bSz, rBound);
buildBlock(layer, l, r);
build(layer+1, l, r, betweenOffs);
}
if (layer == 0) {
buildBetweenZero();
} else {
buildBetween(layer, lBound, rBound, betweenOffs);
}
}
void update(int layer, int lBound, int rBound, int betweenOffs, int x) {
if (layer >= (int)layers.size()) {
return;
}
int bSzLog = (layers[layer]+1) >> 1;
int bSz = 1 << bSzLog;
int blockIdx = (x - lBound) >> bSzLog;
int l = lBound + (blockIdx << bSzLog);
int r = min(l + bSz, rBound);
buildBlock(layer, l, r);
if (layer == 0) {
updateBetweenZero(blockIdx);
} else {
buildBetween(layer, lBound, rBound, betweenOffs);
}
update(layer+1, l, r, betweenOffs, x);
}
inline SqrtTreeItem query(int l, int r, int betweenOffs, int base) {
if (l == r) {
return v[l];
}
if (l + 1 == r) {
return op(v[l], v[r]);
}
int layer = onLayer[clz[(l - base) ^ (r - base)]];
int bSzLog = (layers[layer]+1) >> 1;
int bCntLog = layers[layer] >> 1;
int lBound = (((l - base) >> layers[layer]) << layers[layer]) + base;
int lBlock = ((l - lBound) >> bSzLog) + 1;
int rBlock = ((r - lBound) >> bSzLog) - 1;
SqrtTreeItem ans = suf[layer][l];
if (lBlock <= rBlock) {
SqrtTreeItem add = (layer == 0) ? (
query(n + lBlock, n + rBlock, (1 << lg) - n, n)
) : (
between[layer-1][betweenOffs + lBound + (lBlock << bCntLog) + rBlock]
);
ans = op(ans, add);
}
ans = op(ans, pref[layer][r]);
return ans;
}
public:
inline SqrtTreeItem query(int l, int r) {
return query(l, r, 0, 0);
}
inline void update(int x, const SqrtTreeItem &item) {
v[x] = item;
update(0, 0, n, 0, x);
}
SqrtTree(const vector<SqrtTreeItem>& a)
: n((int)a.size()), lg(log2Up(n)), v(a), clz(1 << lg), onLayer(lg+1) {
clz[0] = 0;
for (int i = 1; i < (int)clz.size(); i++) {
clz[i] = clz[i >> 1] + 1;
}
int tlg = lg;
while (tlg > 1) {
onLayer[tlg] = (int)layers.size();
layers.push_back(tlg);
tlg = (tlg+1) >> 1;
}
for (int i = lg-1; i >= 0; i--) {
onLayer[i] = max(onLayer[i], onLayer[i+1]);
}
int betweenLayers = max(0, (int)layers.size() - 1);
int bSzLog = (lg+1) >> 1;
int bSz = 1 << bSzLog;
indexSz = (n + bSz - 1) >> bSzLog;
v.resize(n + indexSz);
pref.assign(layers.size(), vector<SqrtTreeItem>(n + indexSz));
suf.assign(layers.size(), vector<SqrtTreeItem>(n + indexSz));
between.assign(betweenLayers, vector<SqrtTreeItem>((1 << lg) + bSz));
build(0, 0, n, 0);
}
};
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int n{}, q{};
cin >> n >> q;
vector<pair<int, pii>> ntriv;
for(size_t i = 0; i < n; ++i) {
ll &a = eve[i].first;
ll &b = eve[i].second;
cin >> a >> b;
if(a != 0 && b != 1) {
ntriv.emplace_back(i, eve[i]);
}
}
vector<SqrtTreeItem> gen;
for(size_t i = 0; i < n; ++i) {
if(eve[i].second != 1) gen.push_back({0, eve[i].second, 0, 0});
else gen.push_back({eve[i].first, 1ll, 0, 0});
}
SqrtTree drzewo(gen);
for(size_t i{}; i < q; ++i) {
ll x{}, l{}, r{};
cin >> x >> l >> r;
pair<int, pii> low;
while(l < r) {
low.first = l;
low.second.first = 0;
low.second.second = 0;
auto po = lower_bound(ntriv.begin(), ntriv.end(), low);
if(po == ntriv.end() || po->first >= r) break;
pair<int, pii> it = *po;
if(l <= it.first-1) {
SqrtTreeItem res = drzewo.query(l,it.first-1);
x *= res.mul;
x += res.val;
if(res.over || res.mover || x >= MOD) {
l = it.first;
x %= MOD;
break;
}
}
auto &[ad, mu] = it.second;
x = max(x+ad,x*mu);
if(x >= MOD) {
l = it.first+1;
x %= MOD;
break;
}
l = it.first+1;
}
if(l < r) {
SqrtTreeItem fin = drzewo.query(l, r-1);
x *= fin.mul;
x += fin.val;
x %= MOD;
}
cout << 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 | #include<bits/stdc++.h> using namespace std; using ll = long long; using pii = pair<ll, ll>; constexpr int MAXN = 5e5+2; constexpr ll MOD = 1e9+7; pii eve[MAXN]; //cp-algorithms struct SqrtTreeItem { ll val{}; ll mul{1ll}; bool over{}; bool mover{}; }; SqrtTreeItem op(const SqrtTreeItem &a, const SqrtTreeItem &b) { ll res = a.val*b.mul+b.val; bool ov = (res >= MOD); ov |= a.over; ov |= b.over; bool mov = ((a.mul*b.mul) >= MOD); mov |= a.mover; mov |= b.mover; return SqrtTreeItem{res%MOD,(a.mul*b.mul)%MOD, ov, mov}; } inline int log2Up(int n) { int res = 0; while ((1 << res) < n) { res++; } return res; } class SqrtTree { private: int n, lg, indexSz; vector<SqrtTreeItem> v; vector<int> clz, layers, onLayer; vector< vector<SqrtTreeItem> > pref, suf, between; inline void buildBlock(int layer, int l, int r) { pref[layer][l] = v[l]; for (int i = l+1; i < r; i++) { pref[layer][i] = op(pref[layer][i-1], v[i]); } suf[layer][r-1] = v[r-1]; for (int i = r-2; i >= l; i--) { suf[layer][i] = op(v[i], suf[layer][i+1]); } } inline void buildBetween(int layer, int lBound, int rBound, int betweenOffs) { int bSzLog = (layers[layer]+1) >> 1; int bCntLog = layers[layer] >> 1; int bSz = 1 << bSzLog; int bCnt = (rBound - lBound + bSz - 1) >> bSzLog; for (int i = 0; i < bCnt; i++) { SqrtTreeItem ans; for (int j = i; j < bCnt; j++) { SqrtTreeItem add = suf[layer][lBound + (j << bSzLog)]; ans = (i == j) ? add : op(ans, add); between[layer-1][betweenOffs + lBound + (i << bCntLog) + j] = ans; } } } inline void buildBetweenZero() { int bSzLog = (lg+1) >> 1; for (int i = 0; i < indexSz; i++) { v[n+i] = suf[0][i << bSzLog]; } build(1, n, n + indexSz, (1 << lg) - n); } inline void updateBetweenZero(int bid) { int bSzLog = (lg+1) >> 1; v[n+bid] = suf[0][bid << bSzLog]; update(1, n, n + indexSz, (1 << lg) - n, n+bid); } void build(int layer, int lBound, int rBound, int betweenOffs) { if (layer >= (int)layers.size()) { return; } int bSz = 1 << ((layers[layer]+1) >> 1); for (int l = lBound; l < rBound; l += bSz) { int r = min(l + bSz, rBound); buildBlock(layer, l, r); build(layer+1, l, r, betweenOffs); } if (layer == 0) { buildBetweenZero(); } else { buildBetween(layer, lBound, rBound, betweenOffs); } } void update(int layer, int lBound, int rBound, int betweenOffs, int x) { if (layer >= (int)layers.size()) { return; } int bSzLog = (layers[layer]+1) >> 1; int bSz = 1 << bSzLog; int blockIdx = (x - lBound) >> bSzLog; int l = lBound + (blockIdx << bSzLog); int r = min(l + bSz, rBound); buildBlock(layer, l, r); if (layer == 0) { updateBetweenZero(blockIdx); } else { buildBetween(layer, lBound, rBound, betweenOffs); } update(layer+1, l, r, betweenOffs, x); } inline SqrtTreeItem query(int l, int r, int betweenOffs, int base) { if (l == r) { return v[l]; } if (l + 1 == r) { return op(v[l], v[r]); } int layer = onLayer[clz[(l - base) ^ (r - base)]]; int bSzLog = (layers[layer]+1) >> 1; int bCntLog = layers[layer] >> 1; int lBound = (((l - base) >> layers[layer]) << layers[layer]) + base; int lBlock = ((l - lBound) >> bSzLog) + 1; int rBlock = ((r - lBound) >> bSzLog) - 1; SqrtTreeItem ans = suf[layer][l]; if (lBlock <= rBlock) { SqrtTreeItem add = (layer == 0) ? ( query(n + lBlock, n + rBlock, (1 << lg) - n, n) ) : ( between[layer-1][betweenOffs + lBound + (lBlock << bCntLog) + rBlock] ); ans = op(ans, add); } ans = op(ans, pref[layer][r]); return ans; } public: inline SqrtTreeItem query(int l, int r) { return query(l, r, 0, 0); } inline void update(int x, const SqrtTreeItem &item) { v[x] = item; update(0, 0, n, 0, x); } SqrtTree(const vector<SqrtTreeItem>& a) : n((int)a.size()), lg(log2Up(n)), v(a), clz(1 << lg), onLayer(lg+1) { clz[0] = 0; for (int i = 1; i < (int)clz.size(); i++) { clz[i] = clz[i >> 1] + 1; } int tlg = lg; while (tlg > 1) { onLayer[tlg] = (int)layers.size(); layers.push_back(tlg); tlg = (tlg+1) >> 1; } for (int i = lg-1; i >= 0; i--) { onLayer[i] = max(onLayer[i], onLayer[i+1]); } int betweenLayers = max(0, (int)layers.size() - 1); int bSzLog = (lg+1) >> 1; int bSz = 1 << bSzLog; indexSz = (n + bSz - 1) >> bSzLog; v.resize(n + indexSz); pref.assign(layers.size(), vector<SqrtTreeItem>(n + indexSz)); suf.assign(layers.size(), vector<SqrtTreeItem>(n + indexSz)); between.assign(betweenLayers, vector<SqrtTreeItem>((1 << lg) + bSz)); build(0, 0, n, 0); } }; int main() { ios_base::sync_with_stdio(0); cin.tie(0); int n{}, q{}; cin >> n >> q; vector<pair<int, pii>> ntriv; for(size_t i = 0; i < n; ++i) { ll &a = eve[i].first; ll &b = eve[i].second; cin >> a >> b; if(a != 0 && b != 1) { ntriv.emplace_back(i, eve[i]); } } vector<SqrtTreeItem> gen; for(size_t i = 0; i < n; ++i) { if(eve[i].second != 1) gen.push_back({0, eve[i].second, 0, 0}); else gen.push_back({eve[i].first, 1ll, 0, 0}); } SqrtTree drzewo(gen); for(size_t i{}; i < q; ++i) { ll x{}, l{}, r{}; cin >> x >> l >> r; pair<int, pii> low; while(l < r) { low.first = l; low.second.first = 0; low.second.second = 0; auto po = lower_bound(ntriv.begin(), ntriv.end(), low); if(po == ntriv.end() || po->first >= r) break; pair<int, pii> it = *po; if(l <= it.first-1) { SqrtTreeItem res = drzewo.query(l,it.first-1); x *= res.mul; x += res.val; if(res.over || res.mover || x >= MOD) { l = it.first; x %= MOD; break; } } auto &[ad, mu] = it.second; x = max(x+ad,x*mu); if(x >= MOD) { l = it.first+1; x %= MOD; break; } l = it.first+1; } if(l < r) { SqrtTreeItem fin = drzewo.query(l, r-1); x *= fin.mul; x += fin.val; x %= MOD; } cout << x << '\n'; } } |
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