結果
| 問題 |
No.3143 Colorless Green Parentheses Sleep Furiously
|
| ユーザー |
 yamate11
|
| 提出日時 | 2025-05-16 22:07:37 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 320 ms / 2,000 ms |
| コード長 | 22,134 bytes |
| コンパイル時間 | 4,083 ms |
| コンパイル使用メモリ | 311,140 KB |
| 実行使用メモリ | 23,536 KB |
| 最終ジャッジ日時 | 2025-05-17 00:28:36 |
| 合計ジャッジ時間 | 6,300 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 49 |
ソースコード
#include <bits/stdc++.h>
#include <cassert>
using namespace std;
using ll = long long int;
using u64 = unsigned long long;
using pll = pair<ll, ll>;
// #include <atcoder/all>
// using namespace atcoder;
#define REP(i, a, b) for (ll i = (a); i < (b); i++)
#define REPrev(i, a, b) for (ll i = (a); i >= (b); i--)
#define ALL(coll) (coll).begin(), (coll).end()
#define SIZE(v) ((ll)((v).size()))
#define REPOUT(i, a, b, exp, sep) REP(i, (a), (b)) cout << (exp) << (i + 1 == (b) ? "" : (sep)); cout << "\n"
// @@ !! LIM(tree debug)
// ---- inserted library file tree.cc
struct function_error : runtime_error {
function_error(const string& msg) : runtime_error(msg) {}
};
struct Tree {
struct pe_t {
ll peer;
ll edge;
pe_t(ll peer_ = -1, ll edge_ = -1) : peer(peer_), edge(edge_) {}
static const pe_t end_object;
};
struct nbr_t {
ll parent_idx; // pe[parent_idx] is the parent
vector<pe_t> pe;
nbr_t() : parent_idx(-1), pe() {}
};
template<bool get_peer>
struct nbr_iterator {
const nbr_t& body;
ll pe_idx;
explicit nbr_iterator(const nbr_t& body_, ll pe_idx_) : body(body_), pe_idx(pe_idx_) {
if (pe_idx == body.parent_idx) pe_idx++;
}
auto operator*() const -> typename conditional<get_peer, ll, const pe_t&>::type {
if constexpr (get_peer) return body.pe[pe_idx].peer;
else return body.pe[pe_idx];
}
const nbr_iterator& operator++() {
pe_idx++;
if (pe_idx == body.parent_idx) pe_idx++;
return *this;
}
bool operator !=(const nbr_iterator& o) const { return pe_idx != o.pe_idx; }
};
template<bool get_peer>
struct children_view {
const nbr_t& body;
children_view(const nbr_t& body_) : body(body_) {}
nbr_iterator<get_peer> begin() const { return nbr_iterator<get_peer>(body, 0); }
nbr_iterator<get_peer> end() { return nbr_iterator<get_peer>(body, std::ssize(body.pe)); }
};
ll numNodes;
ll root;
vector<nbr_t> _nbr;
vector<pair<ll, ll>> _edges; // (x, y) in _edges => x < y
vector<ll> _parent; // _parent[root] == -1
vector<ll> _stsize;
vector<ll> _depth;
unordered_map<ll, ll> _edge_idx;
vector<ll> _euler_in;
vector<ll> _euler_out;
vector<pair<ll, bool>> _euler_edge;
vector<vector<vector<ll>>> _lca_tbl;
constexpr static bool use_depth = true;
constexpr static bool use_stsize = true;
constexpr static bool use_euler = true;
Tree(ll numNodes_, ll root_ = 0) : numNodes(numNodes_), root(root_), _nbr(numNodes_) {
if (numNodes == 1) _set_parent();
}
ll add_edge(ll x, ll y) {
ll i = ssize(_edges);
if (i >= numNodes - 1) throw range_error("add_edge");
_nbr[x].pe.emplace_back(y, i);
_nbr[y].pe.emplace_back(x, i);
_edges.emplace_back(min(x, y), max(x, y));
if (i + 1 == numNodes - 1) _set_parent();
return i;
}
void _set_parent() { // called from constructor, add_edge() and change_root()
_nbr[root].parent_idx = ssize(_nbr[root].pe);
if constexpr (use_depth) _depth.resize(numNodes);
if constexpr (use_stsize) _stsize.resize(numNodes);
if constexpr (use_euler) {
_euler_in.resize(numNodes);
_euler_out.resize(numNodes);
_euler_edge.resize(2 * numNodes);
}
ll euler_idx = 0;
auto dfs = [&](auto rF, ll nd, ll pt, ll edge) -> void {
if constexpr (use_depth) _depth[nd] = pt == -1 ? 0 : _depth[pt] + 1;
if constexpr (use_stsize) _stsize[nd] = 1;
if constexpr (use_euler) {
_euler_edge[euler_idx] = {edge, nd < pt};
_euler_in[nd] = euler_idx;
euler_idx++;
}
for (ll i = 0; i < ssize(_nbr[nd].pe); i++) {
auto [c_id, c_eg] = _nbr[nd].pe[i];
if (c_id == pt) _nbr[nd].parent_idx = i;
else {
rF(rF, c_id, nd, c_eg);
if constexpr (use_stsize) _stsize[nd] += _stsize[c_id];
}
}
if constexpr (use_euler) {
_euler_edge[euler_idx] = {edge, pt < nd};
_euler_out[nd] = euler_idx;
euler_idx++;
}
};
dfs(dfs, root, -1, numNodes - 1);
}
pe_t parent_pe(ll nd) { return _nbr[nd].pe[_nbr[nd].parent_idx]; }
ll parent(ll nd) { return nd == root ? -1 : parent_pe(nd).peer; }
ll num_children(ll nd) { return _nbr[nd].pe.size() - (_nbr[nd].parent_idx == (ll)_nbr[nd].pe.size() ? 0 : 1); }
pe_t child_pe(ll nd, ll idx) { return _nbr[nd].pe[idx < _nbr[nd].parent_idx ? idx : idx + 1]; }
ll child(ll nd, ll idx) { return child_pe(nd, idx).peer; }
ll child_edge(ll nd, ll idx) { return child_pe(nd, idx).edge; }
auto children_pe(ll nd) { return children_view<false>(_nbr[nd]); }
auto children(ll nd) { return children_view<true>(_nbr[nd]); }
ll stsize(ll nd) {
if constexpr (use_stsize) return _stsize[nd];
else throw function_error("use_stsize should be set to call stsize.");
}
ll depth(ll nd) {
if constexpr (use_depth) return _depth[nd];
else throw function_error("use_depth should be set to call depth.");
}
ll _enc_node_pair(ll x, ll y) { return (x + 1) * (numNodes + 1) + (y + 1); }
ll edge_idx(ll x, ll y) {
if (_edge_idx.empty()) {
for (ll i = 0; i < ssize(_edges); i++) {
auto [xx, yy] = _edges[i];
_edge_idx[_enc_node_pair(xx, yy)] = i;
_edge_idx[_enc_node_pair(yy, xx)] = i;
}
}
auto it = _edge_idx.find(_enc_node_pair(x, y));
return it == _edge_idx.end() ? -1 : it->second;
}
pair<ll, ll> nodes_of_edge(ll e) { return _edges[e]; }
void _set_euler() {
_euler_in.resize(numNodes);
_euler_out.resize(numNodes);
vector<pair<ll, ll>> stack{{root, -1}};
ll idx = 0;
while (not stack.empty()) {
auto& [nd, cidx] = stack.back();
if (cidx == -1) _euler_in[nd] = idx++;
cidx++;
if (cidx < num_children(nd)) stack.emplace_back(child(nd, cidx), -1);
else {
_euler_out[nd] = idx++;
stack.pop_back();
}
}
}
ll euler_in(ll nd) {
if constexpr (use_euler) return _euler_in[nd];
else throw function_error("use_euler should be set to call euler_in.");
}
ll euler_out(ll nd) {
if constexpr (use_euler) return _euler_out[nd];
else throw function_error("use_euler should be set to call euler_out.");
}
tuple<ll, ll, ll> euler_edge(ll idx) {
if constexpr (use_euler) {
if (idx == 0) return {numNodes - 1, -1, root};
else if (idx == 2 * numNodes - 1) return {numNodes - 1, root, -1};
else {
auto [e, b] = _euler_edge[idx];
auto [x, y] = nodes_of_edge(e);
if (b) swap(x, y);
return {e, x, y};
}
}
else throw function_error("use_euler should be set to call euler_out.");
}
// Lowest Common Ancestor
ll lca(ll x, ll y) {
ll kmax = 1 + bit_width((unsigned)numNodes);
ll lastmove = 2 * numNodes - 2;
if (_lca_tbl.empty()) {
auto choose = [&](const auto& vec, ll a, ll b) -> ll {
if (0 <= b and b <= lastmove and vec[b] >= 0) return depth(vec[a]) < depth(vec[b]) ? vec[a] : vec[b];
else return -1;
};
_lca_tbl.resize(kmax + 1, vector(2, vector(lastmove + 1, -1LL)));
for (ll s = 0; s < 2; s++) for (ll i = 0; i <= lastmove; i++) _lca_tbl[0][s][i] = get<2>(euler_edge(i));
for (ll k = 1; k <= kmax; k++) {
ll prev_len = 1 << (k - 1);
for (ll s = 0; s < 2; s++) {
for (ll i = 0; i <= lastmove; i++) _lca_tbl[k][0][i] = choose(_lca_tbl[k - 1][0], i, i + prev_len);
for (ll i = 0; i <= lastmove; i++) _lca_tbl[k][1][i] = choose(_lca_tbl[k - 1][1], i, i - prev_len);
}
}
}
ll a = euler_in(x), b = euler_in(y);
if (a > b) swap(a, b);
ll k = countr_zero(bit_floor((unsigned)(b - a + 1)));
ll i = _lca_tbl[k][0][a];
ll j = _lca_tbl[k][1][b];
return depth(i) < depth(j) ? i : j;
}
// the path between two nodes (list of nodes, including x and y)
vector<ll> nnpath(ll x, ll y) {
vector<ll> ret;
ll c = lca(x, y);
for ( ; x != c; x = parent(x)) ret.push_back(x);
ret.push_back(c);
ll len = (ll)ret.size();
for ( ; y != c; y = parent(y)) ret.push_back(y);
reverse(ret.begin() + len, ret.end());
return ret;
}
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-but-set-variable"
tuple<ll, ll, ll, ll, ll> diameter() {
if (numNodes == 1) return {0, 0, 0, 0, 0};
if (numNodes == 2) return {1, 0, 1, 0, 1};
depth(root); // to ensure that _depth is correctly built
ll nd0 = max_element(_depth.begin(), _depth.end()) - _depth.begin();
ll nd1 = -1, ct0 = -1, ct1 = -1;
ll diam = 0;
auto dfs2 = [&](auto rF, ll nd, ll dp, ll pt) -> bool {
// DFS from nd0, which is different from the root.
bool ret = false;
ll numChildren = 0;
for (auto [cld, _e] : _nbr[nd].pe) {
if (cld == pt) continue;
numChildren++;
bool bbb = rF(rF, cld, dp + 1, nd);
ret = ret || bbb;
}
if (numChildren > 0) {
if (ret) {
if (diam % 2 == 0) {
if (dp == diam / 2) ct0 = ct1 = nd;
}else {
if (dp == diam / 2) ct0 = nd;
else if (dp == diam / 2 + 1) ct1 = nd;
}
}
}else {
if (dp > diam) {
diam = dp;
nd1 = nd;
ret = true;
}
}
return ret;
};
dfs2(dfs2, nd0, 0, -1);
return {diam, nd0, nd1, ct0, ct1};
}
#pragma GCC diagnostic pop
pair<ll, ll> centroids() {
auto dfs = [&](auto rF, ll nd) -> pair<ll, ll> {
for (ll c : children(nd)) {
ll a = 2 * stsize(c);
if (a > numNodes) return rF(rF, c);
if (a == numNodes) return make_pair(nd, c);
}
return make_pair(nd, -1);
};
return dfs(dfs, root);
}
void change_root(ll newRoot) {
_stsize.clear();
_depth.clear();
_edge_idx.clear();
_euler_in.clear();
_euler_out.clear();
_lca_tbl.clear();
root = newRoot;
_set_parent();
}
};
const Tree::pe_t end_object{-1, -1};
template <typename M>
auto reroot(Tree& tree, const M& unit, auto add, auto mod1, auto mod2) {
using A = decltype(mod2(M(), 0));
vector<A> result(tree.numNodes);
vector<vector<M>> sum_left(tree.numNodes);
vector<vector<M>> sum_right(tree.numNodes);
auto dfs1 = [&](const auto& recF, ll nd) -> A {
ll k = tree.num_children(nd);
vector<M> ws(k);
for (ll i = 0; i < k; i++) {
ll c = tree.child(nd, i);
ws[i] = mod1(recF(recF, c), nd, c);
}
sum_left[nd].resize(k + 1, unit);
sum_right[nd].resize(k + 1, unit);
for (ll i = 0; i < k; i++) sum_left[nd][i + 1] = add(sum_left[nd][i], ws[i]);
for (ll i = k - 1; i >= 0; i--) sum_right[nd][i] = add(sum_right[nd][i + 1], ws[i]);
return mod2(sum_right[nd][0], nd);
};
dfs1(dfs1, tree.root);
auto dfs2 = [&](const auto& recF, ll nd, const M& t) -> void {
result[nd] = mod2(add(sum_right[nd][0], t), nd);
ll k = tree.num_children(nd);
for (ll i = 0; i < k; i++) {
ll c = tree.child(nd, i);
M excl_c = add(sum_left[nd][i], sum_right[nd][i + 1]);
M m_for_c = add(excl_c, t);
A v_for_c = mod2(m_for_c, nd);
M pass_c = mod1(v_for_c, c, nd);
recF(recF, c, pass_c);
}
};
dfs2(dfs2, tree.root, unit);
return result;
}
template <typename M>
vector<M> reroot(Tree& tree, const M& unit, auto add, auto mod1) {
return reroot<M>(tree, unit, add, mod1, [](const M& m, ll i) -> M { return m; });
}
// ---- end tree.cc
// ---- inserted function f:<< from util.cc
// declarations
template <typename T1, typename T2>
ostream& operator<< (ostream& os, const pair<T1,T2>& p);
template <typename T1, typename T2, typename T3>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3>& t);
template <typename T1, typename T2, typename T3, typename T4>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4>& t);
template <typename T1, typename T2, typename T3, typename T4, typename T5>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4,T5>& t);
template <typename T1, typename T2, typename T3, typename T4, typename T5, typename T6>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4,T5,T6>& t);
template <typename T>
ostream& operator<< (ostream& os, const vector<T>& v);
template <typename T, typename C>
ostream& operator<< (ostream& os, const set<T, C>& v);
template <typename T, typename C>
ostream& operator<< (ostream& os, const unordered_set<T, C>& v);
template <typename T, typename C>
ostream& operator<< (ostream& os, const multiset<T, C>& v);
template <typename T1, typename T2, typename C>
ostream& operator<< (ostream& os, const map<T1, T2, C>& mp);
template <typename T1, typename T2, typename C>
ostream& operator<< (ostream& os, const unordered_map<T1, T2, C>& mp);
template <typename T, typename T2>
ostream& operator<< (ostream& os, const queue<T, T2>& orig);
template <typename T, typename T2>
ostream& operator<< (ostream& os, const deque<T, T2>& orig);
template <typename T, typename T2, typename T3>
ostream& operator<< (ostream& os, const priority_queue<T, T2, T3>& orig);
template <typename T>
ostream& operator<< (ostream& os, const stack<T>& st);
#if __cplusplus >= 201703L
template <typename T>
ostream& operator<< (ostream& os, const optional<T>& t);
#endif
ostream& operator<< (ostream& os, int8_t x);
ostream& operator<< (ostream& os, const __int128& x);
// definitions
template <typename T1, typename T2>
ostream& operator<< (ostream& os, const pair<T1,T2>& p) {
os << "(" << p.first << ", " << p.second << ")";
return os;
}
template <typename T1, typename T2, typename T3>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3>& t) {
os << "(" << get<0>(t) << ", " << get<1>(t)
<< ", " << get<2>(t) << ")";
return os;
}
template <typename T1, typename T2, typename T3, typename T4>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4>& t) {
os << "(" << get<0>(t) << ", " << get<1>(t)
<< ", " << get<2>(t) << ", " << get<3>(t) << ")";
return os;
}
template <typename T1, typename T2, typename T3, typename T4, typename T5>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4,T5>& t) {
os << "(" << get<0>(t) << ", " << get<1>(t)
<< ", " << get<2>(t) << ", " << get<3>(t) << ", " << get<4>(t) << ")";
return os;
}
template <typename T1, typename T2, typename T3, typename T4, typename T5, typename T6>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4,T5,T6>& t) {
os << "(" << get<0>(t) << ", " << get<1>(t)
<< ", " << get<2>(t) << ", " << get<3>(t) << ", " << get<4>(t) << ", " << get<5>(t) << ")";
return os;
}
template <typename T>
ostream& operator<< (ostream& os, const vector<T>& v) {
os << '[';
for (auto it = v.begin(); it != v.end(); it++) {
if (it != v.begin()) os << ", ";
os << *it;
}
os << ']';
return os;
}
template <typename T, typename C>
ostream& operator<< (ostream& os, const set<T, C>& v) {
os << '{';
for (auto it = v.begin(); it != v.end(); it++) {
if (it != v.begin()) os << ", ";
os << *it;
}
os << '}';
return os;
}
template <typename T, typename C>
ostream& operator<< (ostream& os, const unordered_set<T, C>& v) {
os << '{';
for (auto it = v.begin(); it != v.end(); it++) {
if (it != v.begin()) os << ", ";
os << *it;
}
os << '}';
return os;
}
template <typename T, typename C>
ostream& operator<< (ostream& os, const multiset<T, C>& v) {
os << '{';
for (auto it = v.begin(); it != v.end(); it++) {
if (it != v.begin()) os << ", ";
os << *it;
}
os << '}';
return os;
}
template <typename T1, typename T2, typename C>
ostream& operator<< (ostream& os, const map<T1, T2, C>& mp) {
os << '[';
for (auto it = mp.begin(); it != mp.end(); it++) {
if (it != mp.begin()) os << ", ";
os << it->first << ": " << it->second;
}
os << ']';
return os;
}
template <typename T1, typename T2, typename C>
ostream& operator<< (ostream& os, const unordered_map<T1, T2, C>& mp) {
os << '[';
for (auto it = mp.begin(); it != mp.end(); it++) {
if (it != mp.begin()) os << ", ";
os << it->first << ": " << it->second;
}
os << ']';
return os;
}
template <typename T, typename T2>
ostream& operator<< (ostream& os, const queue<T, T2>& orig) {
queue<T, T2> que(orig);
bool first = true;
os << '[';
while (!que.empty()) {
T x = que.front(); que.pop();
if (!first) os << ", ";
os << x;
first = false;
}
return os << ']';
}
template <typename T, typename T2>
ostream& operator<< (ostream& os, const deque<T, T2>& orig) {
deque<T, T2> que(orig);
bool first = true;
os << '[';
while (!que.empty()) {
T x = que.front(); que.pop_front();
if (!first) os << ", ";
os << x;
first = false;
}
return os << ']';
}
template <typename T, typename T2, typename T3>
ostream& operator<< (ostream& os, const priority_queue<T, T2, T3>& orig) {
priority_queue<T, T2, T3> pq(orig);
bool first = true;
os << '[';
while (!pq.empty()) {
T x = pq.top(); pq.pop();
if (!first) os << ", ";
os << x;
first = false;
}
return os << ']';
}
template <typename T>
ostream& operator<< (ostream& os, const stack<T>& st) {
stack<T> tmp(st);
os << '[';
bool first = true;
while (!tmp.empty()) {
T& t = tmp.top();
if (first) first = false;
else os << ", ";
os << t;
tmp.pop();
}
os << ']';
return os;
}
#if __cplusplus >= 201703L
template <typename T>
ostream& operator<< (ostream& os, const optional<T>& t) {
if (t.has_value()) os << "v(" << t.value() << ")";
else os << "nullopt";
return os;
}
#endif
ostream& operator<< (ostream& os, int8_t x) {
os << (int32_t)x;
return os;
}
// for Enum type; just displays ordinals.
template <typename E>
typename std::enable_if<std::is_enum<E>::value, std::ostream&>::type
operator<<(std::ostream& os, E e) {
return os << static_cast<typename std::underlying_type<E>::type>(e);
}
// This is a very ad-hoc implementation...
ostream& operator<<(ostream& os, const __int128& v) {
unsigned __int128 a = v < 0 ? -v : v;
ll i = 0;
string s(64, ' ');
if (v == 0) {
s[i++] = '0';
}else {
while (a > 0) {
s[i++] = '0' + (char)(a % 10);
a /= 10;
}
}
if (v < 0) {
s[i++] = '-';
}
s.erase(s.begin() + i, s.end());
reverse(s.begin(), s.end());
os << s;
return os;
}
// ---- end f:<<
// ---- inserted library file debug.cc
template <class... Args>
string dbgFormat(const char* fmt, Args... args) {
size_t len = snprintf(nullptr, 0, fmt, args...);
char buf[len + 1];
snprintf(buf, len + 1, fmt, args...);
return string(buf);
}
template <class Head>
void dbgLog(bool with_nl, Head&& head) {
cerr << head;
if (with_nl) cerr << endl;
}
template <class Head, class... Tail>
void dbgLog(bool with_nl, Head&& head, Tail&&... tail)
{
cerr << head << " ";
dbgLog(with_nl, forward<Tail>(tail)...);
}
#if DEBUG
#define DLOG(...) dbgLog(true, __VA_ARGS__)
#define DLOGNNL(...) dbgLog(false, __VA_ARGS__)
#define DFMT(...) cerr << dbgFormat(__VA_ARGS__) << endl
#define DCALL(func, ...) func(__VA_ARGS__)
#else
#define DLOG(...)
#define DLOGNNL(...)
#define DFMT(...)
#define DCALL(func, ...)
#endif
/*
#if DEBUG_LIB
#define DLOG_LIB(...) dbgLog(true, __VA_ARGS__)
#define DLOGNNL_LIB(...) dbgLog(false, __VA_ARGS__)
#define DFMT_LIB(...) cerr << dbgFormat(__VA_ARGS__) << endl
#define DCALL_LIB(func, ...) func(__VA_ARGS__)
#else
#define DLOG_LIB(...)
#define DFMT_LIB(...)
#define DCALL_LIB(func, ...)
#endif
*/
#define DUP1(E1) #E1 "=", E1
#define DUP2(E1,E2) DUP1(E1), DUP1(E2)
#define DUP3(E1,...) DUP1(E1), DUP2(__VA_ARGS__)
#define DUP4(E1,...) DUP1(E1), DUP3(__VA_ARGS__)
#define DUP5(E1,...) DUP1(E1), DUP4(__VA_ARGS__)
#define DUP6(E1,...) DUP1(E1), DUP5(__VA_ARGS__)
#define DUP7(E1,...) DUP1(E1), DUP6(__VA_ARGS__)
#define DUP8(E1,...) DUP1(E1), DUP7(__VA_ARGS__)
#define DUP9(E1,...) DUP1(E1), DUP8(__VA_ARGS__)
#define DUP10(E1,...) DUP1(E1), DUP9(__VA_ARGS__)
#define DUP11(E1,...) DUP1(E1), DUP10(__VA_ARGS__)
#define DUP12(E1,...) DUP1(E1), DUP11(__VA_ARGS__)
#define GET_MACRO(_1,_2,_3,_4,_5,_6,_7,_8,_9,_10,_11,_12,NAME,...) NAME
#define DUP(...) GET_MACRO(__VA_ARGS__, DUP12, DUP11, DUP10, DUP9, DUP8, DUP7, DUP6, DUP5, DUP4, DUP3, DUP2, DUP1)(__VA_ARGS__)
#define DLOGK(...) DLOG(DUP(__VA_ARGS__))
#define DLOGKL(lab, ...) DLOG(lab, DUP(__VA_ARGS__))
#if DEBUG_LIB
#define DLOG_LIB DLOG
#define DLOGK_LIB DLOGK
#define DLOGKL_LIB DLOGKL
#endif
// ---- end debug.cc
// @@ !! LIM -- end mark --
int main(/* int argc, char *argv[] */) {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout << setprecision(20);
ll N, K; cin >> N >> K;
string S; cin >> S;
ll seq = 0;
ll cur = seq;
vector<ll> par{-1};
for (char c : S) {
if (c == '(') {
ll x = ++seq;
par.push_back(cur);
cur = x;
}else {
if (cur == 0) {
cout << "No\n";
return 0;
}
cur = par[cur];
}
}
if (cur != 0) {
cout << "No\n";
return 0;
}
seq++;
Tree tr(seq);
DLOGK(seq);
REP(i, 1, seq) {
tr.add_edge(par[i], i);
DLOGK(par[i], i);
}
using sta = pair<string, ll>;
auto dfs = [&](auto rF, ll nd) -> sta {
if (tr.num_children(nd) == 0) return {"(1+1)", 2};
string sret;
if (nd != 0) sret = "(";
ll eret = 0;
bool first = true;
for (ll cld : tr.children(nd)) {
auto [s, e] = rF(rF, cld);
if (first) {
sret += move(s);
eret += e;
first = false;
}else {
sret += "+";
sret += move(s);
eret += e;
}
}
if (tr.num_children(nd) == 1) {
sret += "+1";
eret += 1;
}
if (nd != 0) sret += ")";
DLOGKL("ret dfs", nd, sret, eret);
return sta(move(sret), eret);
};
auto [s0, e0] = dfs(dfs, 0);
if (e0 > K) {
cout << "No\n";
return 0;
}
REP(k, 0, K - e0) {
s0 += "+1";
}
cout << "Yes\n" << s0 << "\n";
return 0;
}