#include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 998244353; // constexpr int MOD = 1000000007; constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1}; constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}; constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; template struct SparseTable { using BinOp = std::function; SparseTable() = default; explicit SparseTable(const std::vector& a, const BinOp bin_op) { init(a, bin_op); } void init(const std::vector& a, const BinOp bin_op_) { bin_op = bin_op_; const int n = a.size(); assert(n > 0); lg.assign(n + 1, 0); for (int i = 2; i <= n; ++i) { lg[i] = lg[i >> 1] + 1; } const int table_h = std::countr_zero(std::bit_floor(a.size())) + 1; data.assign(table_h, std::vector(n)); std::copy(a.begin(), a.end(), data.front().begin()); for (int i = 1; i < table_h; ++i) { for (int j = 0; j + (1 << i) <= n; ++j) { data[i][j] = bin_op(data[i - 1][j], data[i - 1][j + (1 << (i - 1))]); } } } Band query(const int left, const int right) const { assert(left < right); const int h = lg[right - left]; return bin_op(data[h][left], data[h][right - (1 << h)]); } private: BinOp bin_op; std::vector lg; std::vector> data; }; template struct SuffixArray { std::vector sa, rank; template explicit SuffixArray(const T& s_, const U sentinel = 0) : s(s_) { const int n = s.size(); s.push_back(sentinel); sa.resize(n + 1); std::iota(sa.rbegin(), sa.rend(), 0); std::ranges::stable_sort( sa, {}, [this](const int index) -> int { return s[index]; }); rank.resize(n + 1); for (int i = 0; i <= n; ++i) { rank[i] = s[i]; } std::vector tmp(n + 1), prev_sa(n + 1); for (int len = 1; len <= n; len <<= 1) { tmp[sa[0]] = 0; for (int i = 1; i <= n; ++i) { if (rank[sa[i - 1]] == rank[sa[i]] && sa[i - 1] + len <= n && rank[sa[i - 1] + (len >> 1)] == rank[sa[i] + (len >> 1)]) { tmp[sa[i]] = tmp[sa[i - 1]]; } else { tmp[sa[i]] = i; } } rank.swap(tmp); std::iota(tmp.begin(), tmp.end(), 0); std::copy(sa.begin(), sa.end(), prev_sa.begin()); for (int i = 0; i <= n; ++i) { const int idx = prev_sa[i] - len; if (idx >= 0) sa[tmp[rank[idx]]++] = idx; } } for (int i = 0; i <= n; ++i) { rank[sa[i]] = i; } } std::vector match(T* t) const { const int lb = lower_bound(t); ++t->back(); const int ub = lower_bound(t); --t->back(); std::vector res(ub - lb); std::copy(sa.begin() + lb, sa.begin() + ub, res.begin()); std::sort(res.begin(), res.end()); return res; } private: T s; int lower_bound(const T* t) const { const int s_size = s.size(), t_size = t->size(); int lb = 0, ub = s_size; while (ub - lb > 1) { const int mid = std::midpoint(lb, ub); int s_idx = sa[mid], t_idx = 0; bool finished = false; for (; s_idx < s_size && t_idx < t_size; ++s_idx, ++t_idx) { if (s[s_idx] != (*t)[t_idx]) { (s[s_idx] < (*t)[t_idx] ? lb : ub) = mid; finished = true; break; } } if (!finished) (s_idx == s_size && t_idx < t_size ? lb : ub) = mid; } return ub; } }; template struct LongestCommonPrefix : SuffixArray { std::vector lcp_array; explicit LongestCommonPrefix(const T& s) : SuffixArray(s) { const int n = s.size(); lcp_array.resize(n); for (int i = 0, common = 0; i < n; ++i) { const int j = this->sa[this->rank[i] - 1]; if (common > 0) --common; while (i + common < n && j + common < n && s[i + common] == s[j + common]) { ++common; } lcp_array[this->rank[i] - 1] = common; } st.init(lcp_array, [](const int a, const int b) -> int { return std::min(a, b); }); } int query(int i, int j) const { assert(i != j); i = this->rank[i]; j = this->rank[j]; if (i > j) std::swap(i, j); return st.query(i, j); } private: SparseTable st; }; template requires requires { typename T::Monoid; typename T::OperatorMonoid; {T::m_id()} -> std::same_as; {T::o_id()} -> std::same_as; {T::m_merge(std::declval(), std::declval())} -> std::same_as; {T::o_merge(std::declval(), std::declval())} -> std::same_as; {T::apply(std::declval(), std::declval())} -> std::same_as; } struct LazySegmentTree { using Monoid = typename T::Monoid; using OperatorMonoid = typename T::OperatorMonoid; explicit LazySegmentTree(const int n) : LazySegmentTree(std::vector(n, T::m_id())) {} explicit LazySegmentTree(const std::vector& a) : n(a.size()), height(std::countr_zero(std::bit_ceil(a.size()))), p2(1 << height) { lazy.assign(p2, T::o_id()); data.assign(p2 << 1, T::m_id()); std::copy(a.begin(), a.end(), data.begin() + p2); for (int i = p2 - 1; i > 0; --i) { data[i] = T::m_merge(data[i << 1], data[(i << 1) + 1]); } } void set(int idx, const Monoid val) { idx += p2; for (int i = height; i > 0; --i) { propagate(idx >> i); } data[idx] = val; for (int i = 1; i <= height; ++i) { const int current_idx = idx >> i; data[current_idx] = T::m_merge(data[current_idx << 1], data[(current_idx << 1) + 1]); } } void apply(int idx, const OperatorMonoid val) { idx += p2; for (int i = height; i > 0; --i) { propagate(idx >> i); } data[idx] = T::apply(data[idx], val); for (int i = 1; i <= height; ++i) { const int current_idx = idx >> i; data[current_idx] = T::m_merge(data[current_idx << 1], data[(current_idx << 1) + 1]); } } void apply(int left, int right, const OperatorMonoid val) { if (right <= left) [[unlikely]] return; left += p2; right += p2; const int ctz_left = std::countr_zero(static_cast(left)); for (int i = height; i > ctz_left; --i) { propagate(left >> i); } const int ctz_right = std::countr_zero(static_cast(right)); for (int i = height; i > ctz_right; --i) { propagate(right >> i); } for (int l = left, r = right; l < r; l >>= 1, r >>= 1) { if (l & 1) apply_sub(l++, val); if (r & 1) apply_sub(--r, val); } for (int i = left >> (ctz_left + 1); i > 0; i >>= 1) { data[i] = T::m_merge(data[i << 1], data[(i << 1) + 1]); } for (int i = right >> (ctz_right + 1); i > 0; i >>= 1) { data[i] = T::m_merge(data[i << 1], data[(i << 1) + 1]); } } Monoid get(int left, int right) { if (right <= left) [[unlikely]] return T::m_id(); left += p2; right += p2; const int ctz_left = std::countr_zero(static_cast(left)); for (int i = height; i > ctz_left; --i) { propagate(left >> i); } const int ctz_right = std::countr_zero(static_cast(right)); for (int i = height; i > ctz_right; --i) { propagate(right >> i); } Monoid res_l = T::m_id(), res_r = T::m_id(); for (; left < right; left >>= 1, right >>= 1) { if (left & 1) res_l = T::m_merge(res_l, data[left++]); if (right & 1) res_r = T::m_merge(data[--right], res_r); } return T::m_merge(res_l, res_r); } Monoid operator[](const int idx) { const int node = idx + p2; for (int i = height; i > 0; --i) { propagate(node >> i); } return data[node]; } template int find_right(int left, const G g) { if (left >= n) [[unlikely]] return n; left += p2; for (int i = height; i > 0; --i) { propagate(left >> i); } Monoid val = T::m_id(); do { while (!(left & 1)) left >>= 1; Monoid nxt = T::m_merge(val, data[left]); if (!g(nxt)) { while (left < p2) { propagate(left); left <<= 1; nxt = T::m_merge(val, data[left]); if (g(nxt)) { val = nxt; ++left; } } return left - p2; } val = nxt; ++left; } while (!std::has_single_bit(static_cast(left))); return n; } template int find_left(int right, const G g) { if (right <= 0) [[unlikely]] return -1; right += p2; for (int i = height; i > 0; --i) { propagate((right - 1) >> i); } Monoid val = T::m_id(); do { --right; while (right > 1 && (right & 1)) right >>= 1; Monoid nxt = T::m_merge(data[right], val); if (!g(nxt)) { while (right < p2) { propagate(right); right = (right << 1) + 1; nxt = T::m_merge(data[right], val); if (g(nxt)) { val = nxt; --right; } } return right - p2; } val = nxt; } while (!std::has_single_bit(static_cast(right))); return -1; } private: const int n, height, p2; std::vector data; std::vector lazy; void apply_sub(const int idx, const OperatorMonoid& val) { data[idx] = T::apply(data[idx], val); if (idx < p2) lazy[idx] = T::o_merge(lazy[idx], val); } void propagate(const int idx) { // assert(1 <= idx && idx < p2); apply_sub(idx << 1, lazy[idx]); apply_sub((idx << 1) + 1, lazy[idx]); lazy[idx] = T::o_id(); } }; namespace monoid { template struct RangeMinimumAndUpdateQuery { using Monoid = T; using OperatorMonoid = T; static constexpr Monoid m_id() { return std::numeric_limits::max(); } static constexpr OperatorMonoid o_id() { return std::numeric_limits::max(); } static Monoid m_merge(const Monoid& a, const Monoid& b) { return std::min(a, b); } static OperatorMonoid o_merge(const OperatorMonoid& a, const OperatorMonoid& b) { return b == o_id() ? a : b; } static Monoid apply(const Monoid& a, const OperatorMonoid& b) { return b == o_id() ? a : b; } }; template struct RangeMaximumAndUpdateQuery { using Monoid = T; using OperatorMonoid = T; static constexpr Monoid m_id() { return std::numeric_limits::lowest(); } static constexpr OperatorMonoid o_id() { return std::numeric_limits::lowest(); } static Monoid m_merge(const Monoid& a, const Monoid& b) { return std::max(a, b); } static OperatorMonoid o_merge(const OperatorMonoid& a, const OperatorMonoid& b) { return b == o_id() ? a : b; } static Monoid apply(const Monoid& a, const OperatorMonoid& b) { return b == o_id()? a : b; } }; template struct RangeMinimumAndAddQuery { using Monoid = T; using OperatorMonoid = T; static constexpr Monoid m_id() { return Inf; } static constexpr OperatorMonoid o_id() { return 0; } static Monoid m_merge(const Monoid& a, const Monoid& b) { return std::min(a, b); } static OperatorMonoid o_merge(const OperatorMonoid& a, const OperatorMonoid& b) { return a + b; } static Monoid apply(const Monoid& a, const OperatorMonoid& b) { return a + b; } }; template struct RangeMaximumAndAddQuery { using Monoid = T; using OperatorMonoid = T; static constexpr Monoid m_id() { return -Inf; } static constexpr OperatorMonoid o_id() { return 0; } static Monoid m_merge(const Monoid& a, const Monoid& b) { return std::max(a, b); } static OperatorMonoid o_merge(const OperatorMonoid& a, const OperatorMonoid& b) { return a + b; } static Monoid apply(const Monoid& a, const OperatorMonoid& b) { return a + b; } }; template struct RangeSumAndUpdateQuery { using Monoid = struct { T sum; int len; }; using OperatorMonoid = T; static std::vector init(const int n) { return std::vector(n, Monoid{0, 1}); } static constexpr Monoid m_id() { return {0, 0}; } static constexpr OperatorMonoid o_id() { return std::numeric_limits::max(); } static Monoid m_merge(const Monoid& a, const Monoid& b) { return Monoid{a.sum + b.sum, a.len + b.len}; } static OperatorMonoid o_merge(const OperatorMonoid& a, const OperatorMonoid& b) { return b == o_id() ? a : b; } static Monoid apply(const Monoid& a, const OperatorMonoid& b) { return Monoid{b == o_id() ? a.sum : b * a.len, a.len}; } }; template struct RangeSumAndAddQuery { using Monoid = struct { T sum; int len; }; using OperatorMonoid = T; static std::vector init(const int n) { return std::vector(n, Monoid{0, 1}); } static constexpr Monoid m_id() { return {0, 0}; } static constexpr OperatorMonoid o_id() { return 0; } static Monoid m_merge(const Monoid& a, const Monoid& b) { return Monoid{a.sum + b.sum, a.len + b.len}; } static OperatorMonoid o_merge(const OperatorMonoid& a, const OperatorMonoid& b) { return a + b; } static Monoid apply(const Monoid& a, const OperatorMonoid& b) { return Monoid{a.sum + b * a.len, a.len}; } }; } // namespace monoid int main() { int n, q; string s; cin >> n >> q >> s; // q = n * (n + 1) / 2; LongestCommonPrefix lcp(s); vector sum(n + 1, 0); REP(i, n + 1) sum[i] = n - lcp.sa[i]; REP(i, n) sum[i + 1] += sum[i]; vector>> queries(n + 1); vector ans(q, 0); REP(i, q) { int l, r; cin >> l >> r; --l; --r; int lb = 0, ub = lcp.rank[l]; while (ub - lb > 1) { const int mid = midpoint(lb, ub); (lcp.query(lcp.sa[mid], l) >= r - l + 1 ? ub : lb) = mid; } ans[i] = ll{lcp.rank[l] - lb} * (r - l); if (lb > 0) ans[i] += sum[lb]; queries[lcp.rank[l]].emplace_back(i, r - l); } LazySegmentTree> seg(monoid::RangeSumAndUpdateQuery::init(n + 1)); // REP(i, n) cout << lcp.lcp_array[i] << " \n"[i + 1 == n]; for (int i = n - 1; i >= 0; --i) { int lb = i, ub = n; while (ub - lb > 1) { const int mid = midpoint(lb, ub); (seg[mid].sum > lcp.lcp_array[i] ? lb : ub) = mid; } seg.apply(i, lb + 1, lcp.lcp_array[i]); // REP(i, n) cout << seg[i].sum << " \n"[i + 1 == n]; for (const auto& [id, mn] : queries[i]) { int lb = i - 1, ub = n; while (ub - lb > 1) { const int mid = midpoint(lb, ub); (seg[mid].sum > mn ? lb : ub) = mid; } ans[id] += (lb - i + 1LL) * mn; ans[id] += seg.get(lb + 1, n).sum; } } REP(i, q) cout << ans[i] << '\n'; return 0; }