This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define INF 0x3f3f3f3f
using namespace std;
const int kN = 1e6;
vector<int> primes[1 + kN];
set<int> pos[1 + kN];
multiset<int> R[1 + kN];
bitset<1 + kN> active;
void minSelf(int &x, int y) {
if (y < x) {
x = y;
}
}
struct ST {
int n;
vector<int> t, leaf;
void init(int N) {
n = N;
int dim = 1;
while (dim < n) {
dim *= 2;
}
t.resize(dim * 2, INF);
leaf.resize(n + 1);
}
void build(int x, int lx, int rx) {
if (lx == rx) {
leaf[lx] = x;
return;
}
int mid = (lx + rx) / 2;
build(x * 2, lx, mid);
build(x * 2 + 1, mid + 1, rx);
}
void update(int pos, int v) {
int x = leaf[pos];
t[x] = v;
do {
x /= 2;
t[x] = min(t[x * 2], t[x * 2 + 1]);
} while (x > 1);
}
int query(int x, int lx, int rx, int st, int dr) {
if (st <= lx && rx <= dr) {
return t[x];
}
int mid = (lx + rx) / 2, ans = INF;
if (st <= mid) {
minSelf(ans, query(x * 2, lx, mid, st, dr));
}
if (mid < dr) {
minSelf(ans, query(x * 2 + 1, mid + 1, rx, st, dr));
}
return ans;
}
int query(int st, int dr) {
return query(1, 1, n, st, dr);
}
} t;
void precalc(int n) {
for (int i = 2; i <= n; ++i) {
if (primes[i].empty()) {
for (int j = i; j <= n; j += i) {
primes[j].emplace_back(i);
}
}
}
}
void rem(int x) {
active[x] = false;
for (int p : primes[x]) {
auto it = pos[p].lower_bound(x);
int left = -1, right = -1;
bool flag = false;
if (it != pos[p].begin()) {
--it;
left = *it;
if (x == *R[left].begin()) {
flag = true;
}
R[left].erase(R[left].find(x));
}
it = pos[p].upper_bound(x);
if (it != pos[p].end()) {
right = *it;
}
if (left != -1 && right != -1) {
if (right < *R[left].begin()) {
flag = true;
}
R[left].emplace(right);
}
if (flag) {
t.update(left, *R[left].begin());
}
pos[p].erase(x);
}
R[x] = {INF};
t.update(x, INF);
}
void add(int x) {
active[x] = true;
for (int p : primes[x]) {
auto it = pos[p].upper_bound(x);
int v = -1;
if (it != pos[p].end()) {
v = *it;
R[x].emplace(v);
}
if (it != pos[p].begin()) {
--it;
bool flag = false;
if (x < *R[*it].begin()) {
flag = true;
}
R[*it].emplace(x);
if (v != -1) {
R[*it].erase(R[*it].find(v));
}
if (flag) {
t.update(*it, *R[*it].begin());
}
}
pos[p].emplace(x);
}
t.update(x, *R[x].begin());
}
void testCase() {
int n, q;
cin >> n >> q;
precalc(n);
for (int i = 1; i <= n; ++i) {
R[i].emplace(INF);
}
t.init(n);
t.build(1, 1, n);
for (int i = 0; i < q; ++i) {
char ch;
cin >> ch;
if (ch == 'S') {
int x;
cin >> x;
if (active[x]) {
rem(x);
} else {
add(x);
}
} else {
int l, r;
cin >> l >> r;
if (t.query(l, r) <= r) {
cout << "DA\n";
} else {
cout << "NE\n";
}
}
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int tests = 1;
for (int tc = 0; tc < tests; ++tc) {
testCase();
}
return 0;
}
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