/** * date : 2022-01-13 01:06:55 */ #define NDEBUG using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; T &x() { return first; } const T &x() const { return first; } U &y() { return second; } const U &y() const { return second; } P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } P operator*(int r) const { return {first * r, second * r}; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } template bool nxp(vector &v) { return next_permutation(begin(v), end(v)); } } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug namespace DebugImpl { template struct is_specialize : false_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } void dump(__int128_t t) { if (t == 0) cerr << 0; if (t < 0) cerr << '-', t = -t; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } void dump(__uint128_t t) { if (t == 0) cerr << 0; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } template ::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template void dump(const T& t, enable_if_t::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template void dump(const pair&); template void dump(const pair&); template void dump(const T& t, enable_if_t::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template void dump(const pair& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template void dump(const pair& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif // macro #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // template struct edge { int src, to; T cost; edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {} edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {} edge &operator=(const int &x) { to = x; return *this; } operator int() const { return to; } }; template using Edges = vector>; template using WeightedGraph = vector>; using UnweightedGraph = vector>; // Input of (Unweighted) Graph UnweightedGraph graph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { UnweightedGraph g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; if (is_1origin) x--, y--; g[x].push_back(y); if (!is_directed) g[y].push_back(x); } return g; } // Input of Weighted Graph template WeightedGraph wgraph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { WeightedGraph g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; cin >> c; if (is_1origin) x--, y--; g[x].emplace_back(x, y, c); if (!is_directed) g[y].emplace_back(y, x, c); } return g; } // Input of Edges template Edges esgraph(int N, int M, int is_weighted = true, bool is_1origin = true) { Edges es; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; es.emplace_back(x, y, c); } return es; } // Input of Adjacency Matrix template vector> adjgraph(int N, int M, T INF, int is_weighted = true, bool is_directed = false, bool is_1origin = true) { vector> d(N, vector(N, INF)); for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; d[x][y] = c; if (!is_directed) d[y][x] = c; } return d; } /** * @brief グラフテンプレート * @docs docs/graph/graph-template.md */ template struct HeavyLightDecomposition { private: void dfs_sz(int cur) { size[cur] = 1; for (auto& dst : g[cur]) { if (dst == par[cur]) { if (g[cur].size() >= 2 && int(dst) == int(g[cur][0])) swap(g[cur][0], g[cur][1]); else continue; } depth[dst] = depth[cur] + 1; par[dst] = cur; dfs_sz(dst); size[cur] += size[dst]; if (size[dst] > size[g[cur][0]]) { swap(dst, g[cur][0]); } } } void dfs_hld(int cur) { down[cur] = id++; for (auto dst : g[cur]) { if (dst == par[cur]) continue; nxt[dst] = (int(dst) == int(g[cur][0]) ? nxt[cur] : int(dst)); dfs_hld(dst); } up[cur] = id; } // [u, v) vector> ascend(int u, int v) const { vector> res; while (nxt[u] != nxt[v]) { res.emplace_back(down[u], down[nxt[u]]); u = par[nxt[u]]; } if (u != v) res.emplace_back(down[u], down[v] + 1); return res; } // (u, v] vector> descend(int u, int v) const { if (u == v) return {}; if (nxt[u] == nxt[v]) return {{down[u] + 1, down[v]}}; auto res = descend(u, par[nxt[v]]); res.emplace_back(down[nxt[v]], down[v]); return res; } public: G& g; int id; vector size, depth, down, up, nxt, par; HeavyLightDecomposition(G& _g, int root = 0) : g(_g), id(0), size(g.size(), 0), depth(g.size(), 0), down(g.size(), -1), up(g.size(), -1), nxt(g.size(), root), par(g.size(), root) { dfs_sz(root); dfs_hld(root); } void build(int root) { dfs_sz(root); dfs_hld(root); } pair idx(int i) const { return make_pair(down[i], up[i]); } template void path_query(int u, int v, bool vertex, const F& f) { int l = lca(u, v); for (auto&& [a, b] : ascend(u, l)) { int s = a + 1, t = b; s > t ? f(t, s) : f(s, t); } if (vertex) f(down[l], down[l] + 1); for (auto&& [a, b] : descend(l, v)) { int s = a, t = b + 1; s > t ? f(t, s) : f(s, t); } } template void path_noncommutative_query(int u, int v, bool vertex, const F& f) { int l = lca(u, v); for (auto&& [a, b] : ascend(u, l)) f(a + 1, b); if (vertex) f(down[l], down[l] + 1); for (auto&& [a, b] : descend(l, v)) f(a, b + 1); } template void subtree_query(int u, bool vertex, const F& f) { f(down[u] + int(!vertex), up[u]); } int lca(int a, int b) { while (nxt[a] != nxt[b]) { if (down[a] < down[b]) swap(a, b); a = par[nxt[a]]; } return depth[a] < depth[b] ? a : b; } int dist(int a, int b) { return depth[a] + depth[b] - depth[lca(a, b)] * 2; } }; /** * @brief Heavy Light Decomposition(重軽分解) * @docs docs/tree/heavy-light-decomposition.md */ // [0, N) の包含関係に関する木 // // 入力 : 区間[L, R) の組 (包含 OK, 交差 NG) // 出力 : g : グラフ // AB : 破壊的, (first, -second) の昇順でソートされる // & AB[0] に超頂点 (-1, N + 1) が入る template vector> inclusion_tree(vector& AB, int N) { int M = AB.size(); AB.emplace_back(-1, N + 1); sort(begin(AB), end(AB), [](auto l, auto r) { return l.first == r.first ? l.second > r.second : l.first < r.first; }); vector> g(M + 1); vector par(M + 1, -1); for (int i = 1; i <= M; i++) { auto [a, b] = AB[i]; int p = i - 1; while (p <= M) { trc(i, p); auto [v, pb] = AB[p]; assert(v <= a); if (b <= pb) break; assert(!(a < pb && pb < b)); p = par[p]; } g[p].push_back(i); par[i] = p; } return g; } // using namespace Nyaan; void Nyaan::solve() { inl(N, Q); ins(S); vp vc; vector a(N); { vi st; rep(j, N) { if (S[j] == ')') { int i = st.back(); st.pop_back(); vc.emplace_back(i, j + 1); a[i] = j, a[j] = i; } else { st.push_back(j); } } } auto g = inclusion_tree(vc, N); HeavyLightDecomposition hld(g); map mp; rep(i, sz(vc)) mp[vc[i]] = i; while (Q--) { ini(u, v); --u, --v; int uu = a[u]; if (u > uu) swap(u, uu); int vv = a[v]; if (v > vv) swap(v, vv); int s = mp[{u, uu + 1}]; int t = mp[{v, vv + 1}]; int l = hld.lca(s, t); if (l == 0) { out(-1); } else { out(vc[l].fi + 1, vc[l].se); } } }