#ifdef LOCAL #include "template.hpp" #else #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; namespace io { template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } template istream &operator>>(istream &is, array &v) { for (auto &x : v) is >> x; return is; } template istream& cin_tuple_impl(istream &is, T &t) { if constexpr (N < std::tuple_size::value) { auto &x = std::get(t); is >> x; cin_tuple_impl(is, t); } return is; } template istream &operator>>(istream &is, tuple &t) { return cin_tuple_impl(is, t); } template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template ostream &operator<<(ostream &os, const array &v) { size_t n = v.size(); for (size_t i = 0; i < n; i++) { if (i) os << " "; os << v[i]; } return os; } template ostream& cout_tuple_impl(ostream &os, const T &t) { if constexpr (N < std::tuple_size::value) { if constexpr (N > 0) os << " "; const auto &x = std::get(t); os << x; cout_tuple_impl(os, t); } return os; } template ostream &operator<<(ostream &os, const tuple &t) { return cout_tuple_impl(os, t); } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } void __attribute__((constructor)) _c() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); } } // namespace io using io::in; using io::out; using io::outr; #define SHOW(x) static_cast(0) using ll = long long; using D = double; using LD = long double; using P = pair; using u8 = uint8_t; using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; using i128 = __int128; using u128 = unsigned __int128; using vi = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) template using PQ = priority_queue>; template using minPQ = priority_queue, greater>; #define rep1(a) for(ll i = 0; i < a; i++) #define rep2(i, a) for(ll i = 0; i < a; i++) #define rep3(i, a, b) for(ll i = a; i < b; i++) #define rep4(i, a, b, c) for(ll i = a; i < b; i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(a) for(ll i = (a)-1; i >= 0; i--) #define rrep2(i, a) for(ll i = (a)-1; i >= 0; i--) #define rrep3(i, a, b) for(ll i = (b)-1; i >= a; i--) #define rrep4(i, a, b, c) for(ll i = (b)-1; i >= a; i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define for_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() ) #define SZ(v) ll(v.size()) #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(c, x) distance((c).begin(), lower_bound(ALL(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(ALL(c), (x))) template T SUM(const vector &v) { T res = 0; for(auto &&a : v) res += a; return res; } template vector> RLE(const vector &v) { if (v.empty()) return {}; T cur = v.front(); int cnt = 1; vector> res; for (int i = 1; i < (int)v.size(); i++) { if (cur == v[i]) cnt++; else { res.emplace_back(cur, cnt); cnt = 1; cur = v[i]; } } res.emplace_back(cur, cnt); return res; } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, true : false); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, true : false); } void YESNO(bool flag) { out(flag ? "YES" : "NO"); } void yesno(bool flag) { out(flag ? "Yes" : "No"); } int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(ll x) { return (__builtin_parityl(x) & 1 ? -1 : 1); } int popcnt_sgn(u64 x) { return (__builtin_parityl(x) & 1 ? -1 : 1); } int highbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int highbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int highbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int highbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template T get_bit(T x, int k) { return x >> k & 1; } template T set_bit(T x, int k) { return x | T(1) << k; } template T reset_bit(T x, int k) { return x & ~(T(1) << k); } template T flip_bit(T x, int k) { return x ^ T(1) << k; } template T popf(deque &que) { T a = que.front(); que.pop_front(); return a; } template T popb(deque &que) { T a = que.back(); que.pop_back(); return a; } template T pop(queue &que) { T a = que.front(); que.pop(); return a; } template T pop(stack &que) { T a = que.top(); que.pop(); return a; } template T pop(PQ &que) { T a = que.top(); que.pop(); return a; } template T pop(minPQ &que) { T a = que.top(); que.pop(); return a; } template ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { ll mid = (ok + ng) / 2; (check(mid) ? ok : ng) = mid; } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 60) { for (int _ = 0; _ < iter; _++) { double mid = (ok + ng) / 2; (check(mid) ? ok : ng) = mid; } return (ok + ng) / 2; } // max x s.t. b*x <= a ll div_floor(ll a, ll b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b - (a % b < 0); } // max x s.t. b*x < a ll div_under(ll a, ll b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b - (a % b <= 0); } // min x s.t. b*x >= a ll div_ceil(ll a, ll b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b + (a % b > 0); } // min x s.t. b*x > a ll div_over(ll a, ll b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b + (a % b >= 0); } // x = a mod b (b > 0), 0 <= x < b ll modulo(ll a, ll b) { assert(b > 0); ll c = a % b; return c < 0 ? c + b : c; } // (q,r) s.t. a = b*q + r, 0 <= r < b (b > 0) // div_floor(a,b), modulo(a,b) pair divmod(ll a, ll b) { ll q = div_floor(a,b); return {q, a - b*q}; } #endif struct Sieve{ vector isprime; vector minfactor; vector mobius; Sieve(int n) : isprime(n+1,true), minfactor(n+1, -1), mobius(n+1,1){ isprime[1] = false; minfactor[1] = 1; for(int i = 2; i <= n; i++){ if(!isprime[i]) continue; minfactor[i] = i; mobius[i] = -1; for(int j = i+i; j <= n; j += i){ isprime[j] = false; if(minfactor[j] == -1) minfactor[j] = i; if((j/i)%i == 0) mobius[j] = 0; else mobius[j] *= -1; } } } vector> factorize(int n){ vector> res; while(n > 1){ int p = minfactor[n]; int e = 0; while(minfactor[n] == p){ n /= p; e++; } res.push_back({p,e}); } return res; } vector divisor(int n){ vector res; res.push_back(1); auto v = factorize(n); for(auto x : v){ int s = res.size(); for(int i = 0; i < s; i++){ int m = 1; for(int _ = 0; _ < x.second; _++){ m *= x.first; res.push_back(res[i]*m); } } } return res; } template void fzt(vector &f){ int n = f.size(); for(int p = 2; p < n; p++){ if(!isprime[p]) continue; for(int q = (n-1)/p; q > 0; q--){ f[q] += f[p*q]; } } } template void fmt(vector &f){ int n = f.size(); // for(int p = 2; p < n; p++){ // if(!isprime[p]) continue; // for(int q = 1; q*p < n; q++){ // f[q] -= f[p*q]; // } // } for(int p = 2; p < n; p++){ if(!isprime[p]) continue; for(int q = (n-1)/p; q > 0; q--){ f[p*q] -= f[q]; } } } template vector conv(const vector &f, const vector &g){ int n = max(f.size(), g.size()); vector nf(n), ng(n), h(n); for(int i = 0; i < (int)f.size(); i++) nf[i] = f[i]; for(int i = 0; i < (int)g.size(); i++) ng[i] = g[i]; fzt(nf); fzt(ng); for(int i = 0; i < n; i++) h[i] = nf[i]*ng[i]; fmt(h); return h; } }; // floor(a/d) == qa, floor(b/d) == qb, d in (l,r] template void enumerate_quotients_pair(T a, T b, F f){ T r = max(a,b); while(r) { T qa = a/r, qb = b/r; T l = max(a/(qa+1), b/(qb+1)); f(l,r,qa,qb); r = l; } } constexpr int MX = 202020; Sieve si(MX); int main(){ ios_base::sync_with_stdio(false); cin.tie(nullptr); vc phi(MX); iota(ALL(phi), 0); si.fmt(phi); vc prf(MX); rep(i,1,MX) prf[i] = prf[i-1] + phi[i]; int t; in(t); ll pre = 0; while(t--){ ll a,b; in(a,b); int l = a^pre, r = b^pre; ll ans = 0; enumerate_quotients_pair(l-1, r, [&](int lb, int ub, int ql, int qr){ if(ql < qr) { ans += prf[ub] - prf[max(1,lb)]; } }); out(ans); pre = ans; } }