// #define _GLIBCXX_DEBUG // #pragma GCC optimize("O2,unroll-loops") #include using namespace std; #define rep(i, n) for (int i = 0; i < int(n); i++) #define per(i, n) for (int i = (n)-1; 0 <= i; i--) #define rep2(i, l, r) for (int i = (l); i < int(r); i++) #define per2(i, l, r) for (int i = (r)-1; int(l) <= i; i--) #define each(e, v) for (auto &e : v) #define MM << " " << #define pb push_back #define eb emplace_back #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define sz(x) (int)x.size() template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } using ll = long long; using pii = pair; using pll = pair; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template using minheap = std::priority_queue, std::greater>; template using maxheap = std::priority_queue; template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } // __int128_t gcd(__int128_t a, __int128_t b) { // if (a == 0) // return b; // if (b == 0) // return a; // __int128_t cnt = a % b; // while (cnt != 0) { // a = b; // b = cnt; // cnt = a % b; // } // return b; // } struct Union_Find_Tree { vector data; const int n; int cnt; Union_Find_Tree(int n) : data(n, -1), n(n), cnt(n) {} int root(int x) { if (data[x] < 0) return x; return data[x] = root(data[x]); } int operator[](int i) { return root(i); } bool unite(int x, int y) { x = root(x), y = root(y); if (x == y) return false; // if (data[x] > data[y]) swap(x, y); data[x] += data[y], data[y] = x; cnt--; return true; } int size(int x) { return -data[root(x)]; } int count() { return cnt; }; bool same(int x, int y) { return root(x) == root(y); } void clear() { cnt = n; fill(begin(data), end(data), -1); } }; template struct Mod_Int { int x; Mod_Int() : x(0) {} Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} static int get_mod() { return mod; } Mod_Int &operator+=(const Mod_Int &p) { if ((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator-=(const Mod_Int &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator*=(const Mod_Int &p) { x = (int)(1LL * x * p.x % mod); return *this; } Mod_Int &operator/=(const Mod_Int &p) { *this *= p.inverse(); return *this; } Mod_Int &operator++() { return *this += Mod_Int(1); } Mod_Int operator++(int) { Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator--() { return *this -= Mod_Int(1); } Mod_Int operator--(int) { Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator-() const { return Mod_Int(-x); } Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; } Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; } Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; } Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; } bool operator==(const Mod_Int &p) const { return x == p.x; } bool operator!=(const Mod_Int &p) const { return x != p.x; } Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod - 2); } Mod_Int pow(long long k) const { Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; } friend istream &operator>>(istream &is, Mod_Int &p) { long long a; is >> a; p = Mod_Int(a); return is; } }; ll mpow(ll x, ll n, ll mod) { ll ans = 1; x %= mod; while (n != 0) { if (n & 1) ans = ans * x % mod; x = x * x % mod; n = n >> 1; } ans %= mod; return ans; } template T modinv(T a, const T &m) { T b = m, u = 1, v = 0; while (b > 0) { T t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return u >= 0 ? u % m : (m - (-u) % m) % m; } ll divide_int(ll a, ll b) { if (b < 0) a = -a, b = -b; return (a >= 0 ? a / b : (a - b + 1) / b); } // const int MOD = 1000000007; const int MOD = 998244353; using mint = Mod_Int; const int inf = 1e9; // ----- library ------- template T Euler_totient(T m) { T ret = m; for (T i = 2; i * i <= m; i++) { if (m % i == 0) ret /= i, ret *= i - 1; while (m % i == 0) m /= i; } if (m > 1) ret /= m, ret *= m - 1; return ret; } template struct Persistent_Segment_Tree { using M = typename Monoid::V; struct Node { Node *lch, *rch; M x; Node(Node *lch, Node *rch, const M &x) : lch(lch), rch(rch), x(x) {} }; int n; unordered_map root; vector used; Persistent_Segment_Tree(const vector &v, int init_id = 0) { resize(v, init_id); } Persistent_Segment_Tree(int n, const M &x, int init_id = 0) { resize(n, x, init_id); } ~Persistent_Segment_Tree() { for (int i = 0; i < (int)used.size(); i++) delete used[i]; } Node *make_node(Node *lch, Node *rch, const M &x) { Node *ret = new Node(lch, rch, x); if (del) used.push_back(ret); return ret; } Node *make_node(const M &x) { return make_node(NULL, NULL, x); } void resize(const vector &v, int init_id = 0) { n = v.size(); root[init_id] = build(v, 0, n); } void resize(int n, const M &x, int init_id = 0) { resize(vector(n, x), init_id); } Node *merge(Node *lch, Node *rch) { return make_node(lch, rch, Monoid::merge(lch->x, rch->x)); } Node *build(const vector &v, int l, int r) { if (r - l == 1) return make_node(v[l]); int m = (l + r) >> 1; return merge(build(v, l, m), build(v, m, r)); } void copy(int ref_id, int new_id) { assert(root.count(ref_id)); root[new_id] = root[ref_id]; } Node *update(int i, const M &x, int l, int r, Node *pre) { if (r - l == 1) return make_node(x); int m = (l + r) >> 1; if (i < m) return merge(update(i, x, l, m, pre->lch), pre->rch); return merge(pre->lch, update(i, x, m, r, pre->rch)); } // ref_id に対応するデータから派生して new_id に対応する新しいデータを作る void update(int ref_id, int new_id, int i, const M &x, bool apply = false) { assert(root.count(ref_id)); root[new_id] = update(i, apply ? Monoid::merge(query(ref_id, i, i + 1), x) : x, 0, n, root[ref_id]); } M query(int a, int b, int l, int r, Node *now) const { if (a >= b || b <= l || r <= a) return Monoid::id; if (a <= l && r <= b) return now->x; int m = (l + r) >> 1; return Monoid::merge(query(a, b, l, m, now->lch), query(a, b, m, r, now->rch)); } M query(int ref_id, int l, int r) { assert(root.count(ref_id)); return query(l, r, 0, n, root[ref_id]); } }; template struct Plus_Monoid { using V = T; static constexpr V merge(const V &a, const V &b) { return a + b; }; static const V id; }; template const T Plus_Monoid::id = 0; // ----- library ------- int main() { ios::sync_with_stdio(false); std::cin.tie(nullptr); cout << fixed << setprecision(15); const int M = 2e5 + 10; vector tos(M); rep2(i, 2, M) tos[i] = Euler_totient(i); Persistent_Segment_Tree> seg(M, 0, M); per2(i, 2, M) { seg.copy(i + 1, i); for (int j = i; j <= M; j += i) seg.update(i, i, j, tos[i], true); } vector sum(M, 0); rep2(i, 2, M) sum[i] = sum[i - 1] + tos[i]; ll prev = 0; int T; cin >> T; while (T--) { ll a, b; cin >> a >> b; ll l = a ^ prev, r = b ^ prev; r++; ll ans = sum[r - l] + seg.query(r - l + 1, l, r); cout << ans << '\n'; prev = ans; } }