#include using namespace std; #define pb push_back #define mp make_pair #define all(x) (x).begin(),(x).end() #define rep(i,n) for(int i=0;i<(n);i++) constexpr int MOD = 1000000007; typedef long long ll; typedef unsigned long long ull; typedef pair pii; constexpr int dx[] = {1, 0, -1, 0, 1, 1, -1, -1}; constexpr int dy[] = {0, -1, 0, 1, 1, -1, -1, 1}; template ostream &operator<<(ostream &os, const vector &vec){os << "["; for (const auto &v : vec) {os << v << ","; } os << "]"; return os; } template ostream &operator<<(ostream &os, const pair &p){os << "(" << p.first << ", " << p.second << ")"; return os;} // \sum_{n = L_i ^ R_i} P - [P / n] * n // (R_i - L_i * 1) * P - \sum_{n = L_i ^ R_i} [P / n] * n set D; set::iterator it; ll solve(ll P, ll l, ll r) { ll ans = (r - l + 1) * P; for(; it != D.end(); it++) { ll l2, r2; ll d = *it; d *= -1; ll ng = P + 1; ll ok = 0; while(ng - ok > 1) { ll c = (ok + ng) / 2; if (P / c >= d) { ok = c; } else { ng = c; } } r2 = ok; ng = P + 1; ok = 0; while(ng - ok > 1) { ll c = (ok + ng) / 2; if (P / c > d) { ok = c; } else { ng = c; } } l2 = ng; if (l2 > r) break; l2 = max(l, l2); r2 = min(r, r2); if (l2 > r2) continue; ans -= d * (l2 + r2) * (r2 - l2 + 1) / 2; } if (it != D.begin()) it--; return ans; } ll solveNaive(ll P, ll l, ll r) { ll ret = 0; for(ll i = l; i <= r; i++) { ret += P % i; } return ret; } void solve() { ll P, Q; cin >> P >> Q; for(ll n = 1; n * n <= P; n++) { D.insert(-n); D.insert(-(P / n)); } it = D.begin(); ll d = (ll)sqrt(P); vector B((P + 1 + d - 1) / d); for (int i = 0; i < B.size(); i++) { ll l = i * d; ll r = (i + 1) * d - 1; B[i] = solve(P, max(1LL, l), r); } for (int q = 0; q < Q; q++) { ll l, r; cin >> l >> r; ll ans = 0; if (r > P) { ans += (r - P) * P; r = P; } if (r - l <= 3 * d) { cout << solveNaive(P, l, r) << endl; continue; } for(; l % d != 0; l++) { ans += P % l; } for(; r % d != 0; r--) { ans += P % r; } ans += P % r; for(int b = l / d; b < r / d; b++) { ans += B[b]; } cout << ans << endl; } } int main() { std::cin.tie(0); std::ios::sync_with_stdio(false); cout.setf(ios::fixed); cout.precision(16); solve(); return 0; }