use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($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, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } // https://github.com/rust-lang-ja/ac-library-rs/blob/master/src/string.rs // Verified by: https://atcoder.jp/contests/abc213/submissions/25662432 fn sa_naive(s: &[T]) -> Vec { let n = s.len(); let mut sa: Vec = (0..n).collect(); sa.sort_by(|&(mut l), &(mut r)| { if l == r { return std::cmp::Ordering::Equal; } while l < n && r < n { if s[l] != s[r] { return s[l].cmp(&s[r]); } l += 1; r += 1; } if l == n { std::cmp::Ordering::Less } else { std::cmp::Ordering::Greater } }); sa } fn sa_doubling(s: &[i32]) -> Vec { let n = s.len(); let mut sa: Vec = (0..n).collect(); let mut rnk: Vec = s.to_vec(); let mut tmp = vec![0; n]; let mut k = 1; while k < n { let cmp = |&x: &usize, &y: &usize| { if rnk[x] != rnk[y] { return rnk[x].cmp(&rnk[y]); } let rx = if x + k < n { rnk[x + k] } else { -1 }; let ry = if y + k < n { rnk[y + k] } else { -1 }; rx.cmp(&ry) }; sa.sort_by(cmp); tmp[sa[0]] = 0; for i in 1..n { tmp[sa[i]] = tmp[sa[i - 1]] + if cmp(&sa[i - 1], &sa[i]) == std::cmp::Ordering::Less { 1 } else { 0 }; } std::mem::swap(&mut tmp, &mut rnk); k *= 2; } sa } trait Threshold { fn threshold_naive() -> usize; fn threshold_doubling() -> usize; } enum DefaultThreshold {} impl Threshold for DefaultThreshold { fn threshold_naive() -> usize { 10 } fn threshold_doubling() -> usize { 40 } } // |returned| = |s| // Complexity: O(|s| upper) #[allow(clippy::cognitive_complexity)] fn sa_is(s: &[usize], upper: usize) -> Vec { let n = s.len(); match n { 0 => return vec![], 1 => return vec![0], 2 => return if s[0] < s[1] { vec![0, 1] } else { vec![1, 0] }, _ => (), } if n < T::threshold_naive() { return sa_naive(s); } if n < T::threshold_doubling() { let s: Vec = s.iter().map(|&x| x as i32).collect(); return sa_doubling(&s); } let mut sa = vec![0; n]; let mut ls = vec![false; n]; for i in (0..n - 1).rev() { ls[i] = if s[i] == s[i + 1] { ls[i + 1] } else { s[i] < s[i + 1] }; } let mut sum_l = vec![0; upper + 1]; let mut sum_s = vec![0; upper + 1]; for i in 0..n { if !ls[i] { sum_s[s[i]] += 1; } else { sum_l[s[i] + 1] += 1; } } for i in 0..=upper { sum_s[i] += sum_l[i]; if i < upper { sum_l[i + 1] += sum_s[i]; } } // sa's origin is 1. let induce = |sa: &mut [usize], lms: &[usize]| { for elem in sa.iter_mut() { *elem = 0; } let mut buf = sum_s.clone(); for &d in lms { if d == n { continue; } let old = buf[s[d]]; buf[s[d]] += 1; sa[old] = d + 1; } buf.copy_from_slice(&sum_l); let old = buf[s[n - 1]]; buf[s[n - 1]] += 1; sa[old] = n; for i in 0..n { let v = sa[i]; if v >= 2 && !ls[v - 2] { let old = buf[s[v - 2]]; buf[s[v - 2]] += 1; sa[old] = v - 1; } } buf.copy_from_slice(&sum_l); for i in (0..n).rev() { let v = sa[i]; if v >= 2 && ls[v - 2] { buf[s[v - 2] + 1] -= 1; sa[buf[s[v - 2] + 1]] = v - 1; } } }; // origin: 1 let mut lms_map = vec![0; n + 1]; let mut m = 0; for i in 1..n { if !ls[i - 1] && ls[i] { lms_map[i] = m + 1; m += 1; } } let mut lms = Vec::with_capacity(m); for i in 1..n { if !ls[i - 1] && ls[i] { lms.push(i); } } assert_eq!(lms.len(), m); induce(&mut sa, &lms); if m > 0 { let mut sorted_lms = Vec::with_capacity(m); for &v in &sa { if lms_map[v - 1] != 0 { sorted_lms.push(v - 1); } } let mut rec_s = vec![0; m]; let mut rec_upper = 0; rec_s[lms_map[sorted_lms[0]] - 1] = 0; for i in 1..m { let mut l = sorted_lms[i - 1]; let mut r = sorted_lms[i]; let end_l = if lms_map[l] < m { lms[lms_map[l]] } else { n }; let end_r = if lms_map[r] < m { lms[lms_map[r]] } else { n }; let same = if end_l - l != end_r - r { false } else { while l < end_l { if s[l] != s[r] { break; } l += 1; r += 1; } l != n && s[l] == s[r] }; if !same { rec_upper += 1; } rec_s[lms_map[sorted_lms[i]] - 1] = rec_upper; } let rec_sa = sa_is::(&rec_s, rec_upper); for i in 0..m { sorted_lms[i] = lms[rec_sa[i]]; } induce(&mut sa, &mut sorted_lms); } for elem in sa.iter_mut() { *elem -= 1; } sa } fn suffix_array_lowercase(s: &[char]) -> Vec { let s: Vec = s.iter().map(|&x| (x as u8 - b'a') as usize).collect(); sa_is::(&s, 25) } // s.len() == sa.len() must hold. // Verified by: https://yukicoder.me/submissions/704334 struct LCP { inv_sa: Vec, spt: Vec>, } impl LCP { pub fn new(s: &[T], sa: &[usize]) -> LCP { let n = sa.len(); assert_eq!(s.len(), n); let mut inv_sa = vec![0; n]; for i in 0..n { inv_sa[sa[i]] = i; } let lcp = Self::create_lcp(s, sa); let spt = Self::create_sparse_table(&lcp); LCP { inv_sa: inv_sa, spt: spt, } } fn create_lcp(s: &[T], sa: &[usize]) -> Vec { let n = s.len(); let mut rank = vec![0; n]; let mut lcp = vec![0; n - 1]; for i in 0..n { rank[sa[i]] = i; } let mut h: usize = 0; for i in 0..n { if rank[i] == 0 { continue; } let j = sa[rank[i] - 1]; h = h.saturating_sub(1); while j + h < n && i + h < n { if s[j + h] != s[i + h] { break; } h += 1; } lcp[rank[i] - 1] = h; } return lcp; } fn create_sparse_table(lcp: &[usize]) -> Vec> { let n = lcp.len(); let mut h: usize = 1; while (1 << h) <= n { h += 1; } let mut st: Vec> = vec![Vec::new(); h]; st[0] = Vec::from(lcp); for j in 1 .. h { st[j] = vec![0; n + 1 - (1 << j)]; for i in 0 .. n + 1 - (1 << j) { st[j][i] = std::cmp::min( st[j - 1][i], st[j - 1][i + 1_usize.wrapping_shl(j as u32 - 1)]); } } return st; } pub fn get_lcp(&self, f: usize, s: usize) -> usize { let n = self.inv_sa.len(); if f == n || s == n { return 0; } let f = self.inv_sa[f]; let s = self.inv_sa[s]; let (f, s) = if f > s { (s, f) } else { (f, s) }; assert!(f < s); let usize_size = usize::max_value().count_ones(); let diff = usize_size - 1 - (s - f).leading_zeros(); // topmost 1 return std::cmp::min(self.spt[diff as usize][f], self.spt[diff as usize][s - 1_usize.wrapping_shl(diff)]); } } // Lazy Segment Tree. This data structure is useful for fast folding and updating on intervals of an array // whose elements are elements of monoid T. Note that constructing this tree requires the identity // element of T and the operation of T. This is monomorphised, because of efficiency. T := i64, biop = max, upop = (+) // Reference: https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp // Verified by: https://judge.yosupo.jp/submission/68794 // https://atcoder.jp/contests/joisc2021/submissions/27734236 pub trait ActionRing { type T: Clone + Copy; // data type U: Clone + Copy + PartialEq + Eq; // action fn biop(x: Self::T, y: Self::T) -> Self::T; fn update(x: Self::T, a: Self::U) -> Self::T; fn upop(fst: Self::U, snd: Self::U) -> Self::U; fn e() -> Self::T; fn upe() -> Self::U; // identity for upop } pub struct LazySegTree { n: usize, dep: usize, dat: Vec, lazy: Vec, } impl LazySegTree { pub fn new(n_: usize) -> Self { let mut n = 1; let mut dep = 0; while n < n_ { n *= 2; dep += 1; } // n is a power of 2 LazySegTree { n: n, dep: dep, dat: vec![R::e(); 2 * n], lazy: vec![R::upe(); n], } } #[allow(unused)] pub fn with(a: &[R::T]) -> Self { let mut ret = Self::new(a.len()); let n = ret.n; for i in 0..a.len() { ret.dat[n + i] = a[i]; } for i in (1..n).rev() { ret.update_node(i); } ret } #[inline] pub fn set(&mut self, idx: usize, x: R::T) { debug_assert!(idx < self.n); self.apply_any(idx, |_t| x); } #[inline] pub fn apply(&mut self, idx: usize, f: R::U) { debug_assert!(idx < self.n); self.apply_any(idx, |t| R::update(t, f)); } pub fn apply_any R::T>(&mut self, idx: usize, f: F) { debug_assert!(idx < self.n); let idx = idx + self.n; for i in (1..self.dep + 1).rev() { self.push(idx >> i); } self.dat[idx] = f(self.dat[idx]); for i in 1..self.dep + 1 { self.update_node(idx >> i); } } pub fn get(&mut self, idx: usize) -> R::T { debug_assert!(idx < self.n); let idx = idx + self.n; for i in (1..self.dep + 1).rev() { self.push(idx >> i); } self.dat[idx] } /* [l, r) (note: half-inclusive) */ #[inline] pub fn query(&mut self, rng: std::ops::Range) -> R::T { let (l, r) = (rng.start, rng.end); debug_assert!(l <= r && r <= self.n); if l == r { return R::e(); } let mut l = l + self.n; let mut r = r + self.n; for i in (1..self.dep + 1).rev() { if ((l >> i) << i) != l { self.push(l >> i); } if ((r >> i) << i) != r { self.push((r - 1) >> i); } } let mut sml = R::e(); let mut smr = R::e(); while l < r { if (l & 1) != 0 { sml = R::biop(sml, self.dat[l]); l += 1; } if (r & 1) != 0 { r -= 1; smr = R::biop(self.dat[r], smr); } l >>= 1; r >>= 1; } R::biop(sml, smr) } /* ary[i] = upop(ary[i], v) for i in [l, r) (half-inclusive) */ #[inline] pub fn update(&mut self, rng: std::ops::Range, f: R::U) { let (l, r) = (rng.start, rng.end); debug_assert!(l <= r && r <= self.n); if l == r { return; } let mut l = l + self.n; let mut r = r + self.n; for i in (1..self.dep + 1).rev() { if ((l >> i) << i) != l { self.push(l >> i); } if ((r >> i) << i) != r { self.push((r - 1) >> i); } } { let l2 = l; let r2 = r; while l < r { if (l & 1) != 0 { self.all_apply(l, f); l += 1; } if (r & 1) != 0 { r -= 1; self.all_apply(r, f); } l >>= 1; r >>= 1; } l = l2; r = r2; } for i in 1..self.dep + 1 { if ((l >> i) << i) != l { self.update_node(l >> i); } if ((r >> i) << i) != r { self.update_node((r - 1) >> i); } } } #[inline] fn update_node(&mut self, k: usize) { self.dat[k] = R::biop(self.dat[2 * k], self.dat[2 * k + 1]); } fn all_apply(&mut self, k: usize, f: R::U) { self.dat[k] = R::update(self.dat[k], f); if k < self.n { self.lazy[k] = R::upop(self.lazy[k], f); } } fn push(&mut self, k: usize) { let val = self.lazy[k]; self.all_apply(2 * k, val); self.all_apply(2 * k + 1, val); self.lazy[k] = R::upe(); } } enum Affine {} type AffineInt = i64; // Change here to change type impl ActionRing for Affine { type T = (AffineInt, AffineInt); // data, size type U = (AffineInt, AffineInt); // action, (a, b) |-> x |-> ax + b fn biop((x, s): Self::T, (y, t): Self::T) -> Self::T { (x + y, s + t) } fn update((x, s): Self::T, (a, b): Self::U) -> Self::T { (x * a + b * s, s) } fn upop(fst: Self::U, snd: Self::U) -> Self::U { let (a, b) = fst; let (c, d) = snd; (a * c, b * c + d) } fn e() -> Self::T { (0.into(), 0.into()) } fn upe() -> Self::U { // identity for upop (1.into(), 0.into()) } } fn main() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););} input! { n: usize, q: usize, s: chars, lr: [(usize1, usize); q], } let sa = suffix_array_lowercase(&s); let mut acc = vec![0; n + 1]; for i in 0..n { acc[i + 1] = acc[i] + (n - sa[i]) as i64; } let lcp = LCP::new(&s, &sa); let mut right_vals = vec![0; n + 1]; let mut st = LazySegTree::::new(n); let mut stc = LazySegTree::::new(n); for i in 0..n { st.set(i, (0, 1)); stc.set(i, (0, 1)); } for i in (0..n).rev() { let cur = if i == n - 1 { 0 } else { lcp.get_lcp(sa[i], sa[i + 1]) }; let count = st.query(cur + 1..n).0; st.update(cur + 1..n, (0, 0)); stc.update(cur + 1..n, (0, 0)); st.update(cur..cur + 1, (1, count + 1)); stc.update(cur..cur + 1, (1, (count + 1) * cur as i64)); right_vals[i] = stc.query(0..n).0; } // eprintln!("right_vals = {:?}", right_vals); for (l, r) in lr { let len = r - l; let left = { let mut pass = 0; let mut fail = lcp.inv_sa[l] + 1; while fail - pass > 1 { let mid = (fail + pass) / 2; if lcp.get_lcp(sa[lcp.inv_sa[l] - mid], l) >= len { pass = mid; } else { fail = mid; } } pass }; let right = { let mut pass = 1; let mut fail = n - lcp.inv_sa[l] + 1; while fail - pass > 1 { let mid = (fail + pass) / 2; if lcp.get_lcp(sa[lcp.inv_sa[l] + mid - 1], l) >= len { pass = mid; } else { fail = mid; } } pass }; let mut ans = acc[lcp.inv_sa[l] - left]; // [0, lcp.inv_sa[l] - left) ans += (left + right) as i64 * (len - 1) as i64; // [lcp.inv_sa[l] - left, lcp.inv_sa[l] + right) // [lcp.inv_sa[l] + right, n) ans += right_vals[lcp.inv_sa[l] + right - 1]; puts!("{}\n", ans); } }