#include // #include // #include // #include // #include using namespace std; using ll = long long; using VI = vector; using VL = vector; using VD = vector; using VS = vector; using VB = vector; using VVB = vector>; using VVI = vector; using VVL = vector; using VVD = vector; using VVVI = vector; using VVVL = vector; using VVVD = vector; using PII = std::pair; using VPII = std::vector>; using PLL = std::pair; using VPLL = std::vector>; using TI3 = std::tuple; using TI4 = std::tuple; using TL3 = std::tuple; using TL4 = std::tuple; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repr(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep2(i, s, n) for (int i = (s); i < (int)(n); i++) #define repr2(i, g, n) for (int i = (int)(n)-1; i >= (g); i--) #define rep3(i, s, n, d) for (int i = (s); i < (int)(n); i += (d)) #define allpt(v) (v).begin(), (v).end() #define allpt_c(v) (v).cbegin(), (v).cend() #define allpt_r(v) (v).rbegin(), (v).rend() #define allpt_cr(v) (v).crbegin(), (v).crend() const int mod1 = 1e9 + 7, mod2 = 998244353, mod3 = 1e9 + 9; const int mod = mod1; const ll inf = 1e18; const int infint = 1e9; const string wsp = " "; const string tb = "\t"; const string rt = "\n"; const string alphabets = "abcdefghijklmnopqrstuvwxyz"; template void show1dvec(const vector &v) { if (v.size() == 0) return; int n = v.size() - 1; rep(i, n) cout << v[i] << wsp; cout << v[n] << rt; return; } int get1dcoodinate(int w, int i, int j) { return i * w + j; } template ostream &operator<<(ostream &os, const vector &v) { if (v.size() == 0) return os; int n = v.size() - 1; rep(i, n) os << v[i] << wsp; os << v[n] << rt; return os; } template istream &operator>>(istream &is, vector &v) { if (v.size() == 0) return is; int n = v.size(); rep(i, n) is >> v[i]; return is; } template ostream &operator<<(ostream &os, const vector> &v) { if (v.size() == 0) return os; int n = v.size(); rep(i, n) os << v[i]; return os; } template istream &operator>>(istream &is, vector> &v) { if (v.size() == 0) return is; int n = v.size(); rep(i, n) is >> v[i]; return is; } template istream &operator>>(istream &is, vector> &v) { if (v.size() == 0) return is; int n = v.size(); rep(i, n) is >> v[i].first >> v[i].second; return is; } template ostream &operator<<(ostream &os, const vector> &v) { if (v.size() == 0) return os; int n = v.size(); rep(i, n) os << v[i].first << v[i].second << rt; return os; } void show2dvec(const vector &v) { int n = v.size(); rep(i, n) cout << v[i] << rt; } template void show2dvec(const vector> &v) { int n = v.size(); rep(i, n) show1dvec(v[i]); } template void range_sort(vector &arr, int l, int r) { sort(arr.begin() + l, arr.begin() + r); } template void show1dpair(const vector> &v) { int n = v.size(); rep(i, n) cout << v[i].first << wsp << v[i].second << rt; return; } template void pairzip(const vector> &v, vector &t, vector &s) { int n = v.size(); rep(i, n) { t.push_back(v[i].first); s.push_back(v[i].second); } return; } template void maxvec(vector &v) { T s = v[0]; int n = v.size(); rep(i, n - 1) { if (s > v[i + 1]) { v[i + 1] = s; } s = v[i + 1]; } } template bool myfind(T t, S s) { return find(t.cbegin(), t.cend(), s) != t.cend(); } bool check(int y, int x, int h, int w) { return 0 <= y && y < h && 0 <= x && x < w; } bool iskadomatsu(int a, int b, int c) { return (a != b && b != c && c != a) && ((a > b && b < c) || (a < b && b > c)); } double euc_dist(PII a, PII b) { return sqrt(pow(a.first - b.first, 2) + pow(a.second - b.second, 2)); } // VS split(string s, char c) { // VS ret; // string part; // s += c; // rep(i, s.length()) { // if (s[i] == c) { // if (part != "") ret.emplace_back(part); // part = ""; // } else if (s[i] != c) { // part += s[i]; // } // } // return ret; // } VS split(string s, char c, char d) { VS ret; reverse(allpt(s)); string part; s += c; rep(i, s.length()) { if (s[i] == c) { if (part != "") { string t; t += c; ret.emplace_back(t); ret.emplace_back(part); } part = ""; } else if (s[i] == d) { if (part != "") { string t; t += d; ret.emplace_back(t); ret.emplace_back(part); } part = ""; } else { part += s[i]; } } return ret; } template ll pow_mod(T p, S q, R mod = 1ll) { ll ret = 1, r = p; while (q) { if (q % 2) ret *= r, ret %= mod; r = (r * r) % mod, q /= 2; } return ret % mod; } template ll pow_no_mod(T p, S q) { ll ret = 1, r = p; while (q) { if (q % 2) ret *= r; r = (r * r), q /= 2; } return ret; } void make_frac_tables(VL &frac_list, VL &frac_inv_list) { rep(i, frac_list.size() - 1) { frac_list[i + 1] *= frac_list[i] * (i + 1); frac_list[i + 1] %= mod; frac_inv_list[i + 1] *= frac_inv_list[i] * pow_mod(i + 1, mod - 2, mod); frac_inv_list[i + 1] %= mod; } } pair make_frac_tables(int n) { VL frac_list(n + 1, 1), frac_inv_list(n + 1, 1); rep(i, n) { frac_list[i + 1] *= frac_list[i] * (i + 1); frac_list[i + 1] %= mod; frac_inv_list[i + 1] *= frac_inv_list[i] * pow_mod(i + 1, mod - 2, mod); frac_inv_list[i + 1] %= mod; } return make_pair(frac_list, frac_inv_list); } ll comb(int a, int b, const VL &frac_list, const VL &frac_inv_list) { if (a < b) return 0; if (b < 0) return 0; ll ret = frac_list[a]; ret *= frac_inv_list[b]; ret %= mod; ret *= frac_inv_list[a - b]; ret %= mod; return ret; } struct vec2d { ll x; ll y; vec2d(ll _x, ll _y) { x = _x; y = _y; } ll dot(vec2d p) { return x * p.x + y * p.y; } vec2d diff(vec2d p) { return vec2d(x - p.x, y - p.y); } }; struct node { int parent = -1; ll weight = 0; int depth = 0; int black = 1; int white = 0; int subtree = 1; VPII children; VPII connect; node(int n) { parent = -1; weight = 0; depth = 0; black = 1; white = 0; subtree = 1; children; connect; } }; struct graph { int _n; int root = 0; vector nodes; graph(int n) { _n = n; rep(i, _n) nodes.emplace_back(node(_n)); } void getconnect0_1() { int a, b; cin >> a >> b; nodes[a].connect.emplace_back(b, 0); nodes[b].connect.emplace_back(a, 0); } void getconnect0_2() { int a, b, c; cin >> a >> b >> c; nodes[a].connect.emplace_back(b, c); nodes[b].connect.emplace_back(a, c); } void getconnect1_1() { int a, b; cin >> a >> b; a--, b--; nodes[a].connect.emplace_back(b, 0); nodes[b].connect.emplace_back(a, 0); } void getconnect1_2() { int a, b, c; cin >> a >> b >> c; a--, b--; nodes[a].connect.emplace_back(b, c); nodes[b].connect.emplace_back(a, c); } void showparent() { rep(i, _n - 1) cout << nodes[i].parent << wsp; cout << nodes[_n - 1].parent << rt; } void showweight() { rep(i, _n - 1) cout << nodes[i].weight << wsp; cout << nodes[_n - 1].weight << rt; } void showsubtree() { rep(i, _n - 1) cout << nodes[i].subtree << wsp; cout << nodes[_n - 1].subtree << rt; } void showdepth() { rep(i, _n - 1) cout << nodes[i].depth << wsp; cout << nodes[_n - 1].depth << rt; } }; struct point { int x; int y; point() { x = 0; y = 0; } point(int _x, int _y) { x = _x; y = _y; } void pointinput() { int _x, _y; cin >> _x >> _y; x = _x; y = _y; } void pointinv() { swap(x, y); } }; double pointseuc(point a, point b) { ll ax = a.x, bx = b.x, ay = a.y, by = b.y; return sqrt(pow(ax - bx, 2) + pow(ay - by, 2)); } ll pointseucsquare(point a, point b) { ll ax = a.x, bx = b.x, ay = a.y, by = b.y; return (ax - bx) * (ax - bx) + (ay - by) * (ay - by); } int pointsmanhattan(point a, point b) { return abs(a.x - b.x) + abs(a.y - b.y); } double dist_segment_point(TL3 segment, point p) { double a = get<0>(segment); double b = get<1>(segment); double c = get<2>(segment); return abs(a * p.x + b * p.y - c) / (a * a + b * b + c * c); } TL3 segment_parameter(point p, point q) { ll a, b, c; a = q.y - p.y; b = p.x - q.x; c = a * p.x + b * p.y; TL3 ret = (TL3){a, b, c}; // cout << a << b << c << rt; return ret; } int cross_check(TL3 segment, point p) { ll a = get<0>(segment); ll b = get<1>(segment); ll c = get<2>(segment); auto f = a * p.x + b * p.y - c; int ret; if (f > 0) ret = 1; if (f == 0) ret = 0; if (f < 0) ret = -1; return ret; } void shave(vector &v, int n) { if (n <= 1) return; vector w(n + 1, true); int x; w[0] = w[1] = false; rep2(i, 2, n + 1) { if (w[i]) { x = i * 2; while (x <= n) { w[x] = false; x += i; } } } rep(i, n + 1) if (w[i]) v.emplace_back(i); } template void coordinate_compress(vector &x, map &zip, int &xs) { sort(x.begin(), x.end()); x.erase(unique(x.begin(), x.end()), x.end()); xs = x.size(); for (int i = 0; i < xs; i++) { zip[x[i]] = i; } } // ll getpalindrome(int l, int r, const string &s, VL &memo) { // if (r - l <= 1) return 1; // if (memo[l] != -1) return memo[l]; // ll ret{1}; // int n = (r - l) / 2; // string sl, sr; // rep(i, n) { // sl += s[l + i]; // sr += s[r - 1 - i]; // string rsr(i + 1, '0'); // reverse_copy(allpt_c(sr), rsr.begin()); // // cout << sl << wsp << sr << wsp << rsr << rt; // if (sl == rsr) { // ret += getpalindrome(l + i + 1, r - i - 1, s, memo); // ret %= mod; // } // } // memo[l] = ret; // return ret; // } void getpalindrome(int l, int r, int n, const string &s, VVB &memo) { if (r - l <= 1 || s[l] == s[r - 1]) { memo[l][r] = true; if (l > 0 && r < n) { getpalindrome(l - 1, r + 1, n, s, memo); } } return; } // void djcstra(graph graphs, int s, int t) { // const int n = graphs._n; // VL shortest(n, inf); // shortest[s] = 0; // priority_queue> pq; // pq.push(make_pair(0, s)); // while (!pq.empty()) { // auto [t, v] = pq.top(); // pq.pop(); // t = -t; // if (shortest[v] != t) continue; // for (auto [u, c] : graphs.nodes[v].connect) { // if (t + c < shortest[u]) { // shortest[u] = t + c; // pq.push(make_pair(-(t + c), u)); // } // } // } // } int main() { cin.tie(0); ios::sync_with_stdio(false); // リアクティブ問題のときはコメントアウト #ifdef DEBUG cout << "DEBUG MODE" << endl; // ifstream in("input.txt"); // for debug // cin.rdbuf(in.rdbuf()); // for debug chrono::system_clock::time_point timestart, timeend; // for debug timestart = std::chrono::system_clock::now(); // for debug #endif int p, q, n, m; ll ans{0}; cin >> p >> q; VPII query(q); cin >> query; if (p <= 30) { VL v(p + 1, 0); rep2(i, 1, p + 1) { v[i] = p % i + v[i - 1]; } for (auto [a, b] : query) { ans = 0; if (b > p) { ans += 1ll * p * (b - p); b = p; } ans += v[b] - v[a - 1]; // cout << (VI){a, b}; cout << ans << rt; } } else { VL u, u_ini, u_diff, u_sum, v; rep2(i, 1, 100000) { auto c = p / i; if (u.empty() || c + 1 < u.back()) { u.emplace_back(c + 1); } else { break; } } reverse(allpt(u)); m = u.size(); // cout << u; n = u[0] - 1; v.resize(n + 1), u_ini.resize(m), u_sum.resize(m), u_diff.resize(m); fill(allpt(v), 0), fill(allpt(u_ini), 0), fill(allpt(u_sum), 0), fill(allpt(u_diff), 0); rep2(i, 1, n + 1) { v[i] = p % i + v[i - 1]; } rep(i, m - 1) { u_ini[i] = p % (u[i + 1] - 1); u_diff[i] = m - 1 - i; auto d = u[i + 1] - u[i]; u_sum[i] = d * (d - 1) / 2 * u_diff[i] + d * u_ini[i]; } rep(i, m - 1) u_sum[i + 1] += u_sum[i]; // cout << u_ini << u_diff << u_sum; for (auto [a, b] : query) { ans = 0; if (a > p) { ans = 1ll * p * abs(b - a + 1); } else if (b <= n) { ans += v[b] - v[a - 1]; } else { if (b > p) { ans += 1ll * p * max(b - p, 0); b = p; } if (a <= n) { ans += v[n] - v[a - 1]; a = n + 1; } auto vl = v.size(); auto l = upper_bound(allpt_c(u), a) - u.cbegin() - 1; auto r = upper_bound(allpt_c(u), b) - u.cbegin() - 1; // cout << (VI){a, b, l, r, (int)u_ini[l], (int)u_ini[r]}; if (l == r) { auto lr = r - l + 1; ans += 1ll * (p % a + p % b) * (b - a + 1) / 2; } else { ans += 1ll * (p % a + p % u[l]) * (u[l] - a + 1) / 2; // cout << ans << rt; ans += 1ll * (p % b + p % u[r]) * (b - u[r] + 1) / 2; // cout << ans << rt; ans += u_sum[r - 1] - u_sum[l]; } } cout << ans << rt; } } #ifdef DEBUG timeend = chrono::system_clock::now(); auto elapsed = chrono::duration_cast(timeend - timestart) .count(); cout << "Time is " << elapsed << "ms" << std::endl; #endif return 0; }