#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); let mut next = || { iter.next().unwrap() }; input_inner!{next, $($r)*} }; ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes .by_ref() .map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr, ) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ( $(read_value!($next, $t)),* ) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => { read_value!($next, usize) - 1 }; ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); (0..len).map(|_| read_value!($next, $t)).collect::>() }}; ($next:expr, $t:ty) => { $next().parse::<$t>().expect("Parse error") }; } fn solve() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts { ($format:expr) => (write!(out,$format).unwrap()); ($format:expr, $($args:expr),+) => (write!(out,$format,$($args),*).unwrap()) } input! { p: i64, q: usize, lr: [(i64, i64); q], } let mut tbl = vec![(0i64, 0i64, 0i64, 0i64)]; let k = (p as f64).sqrt() as i64; for i in 1 .. p / k + 1 { let last = tbl[tbl.len() - 1].1; tbl.push((i, last + (p % i), 0, 0)); // 0, 0: don't care } for i in (1 .. k).rev() { let l = p / (i + 1); let r = p / i; let last = tbl[tbl.len() - 1].1; // delta = \sum_{j=l+1}^{r} (p % j) = \sum_{j=i+1}^{r} (p - i * j) let delta = (2 * p - i * (l + r + 1)) * (r - l) / 2; tbl.push((r, last + delta, i, p - i * r)); } // eprintln!("tbl = {:?}", tbl); macro_rules! sum { ($k: expr) => {{ let mut ans = 0; let mut k = $k; if k > p { ans += p * (k - p); k = p; } let idx = match tbl.binary_search(&(k, -1, -1, -1)) { Ok(_) => panic!(), Err(idx) => idx, }; let (start, acc, d, b) = tbl[idx]; let diff = start - k; ans + acc - b * diff - d * (diff * (diff - 1) / 2) }}; } for (l, r) in lr { puts!("{}\n", sum!(r) - sum!(l - 1)); } } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); }