#ifndef HIDDEN_IN_VS // 折りたたみ用 // 警告の抑制 #define _CRT_SECURE_NO_WARNINGS // ライブラリの読み込み #include using namespace std; // 型名の短縮 using ll = long long; // -2^63 ~ 2^63 = 9 * 10^18(int は -2^31 ~ 2^31 = 2 * 10^9) using pii = pair; using pll = pair; using pil = pair; using pli = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vvvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vvvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; template using priority_queue_rev = priority_queue, greater>; using Graph = vvi; // 定数の定義 const double PI = acos(-1); const vi DX = { 1, 0, -1, 0 }; // 4 近傍(下,右,上,左) const vi DY = { 0, 1, 0, -1 }; int INF = 1001001001; ll INFL = 4004004003104004004LL; // (int)INFL = 1010931620; double EPS = 1e-15; // 入出力高速化 struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; // 汎用マクロの定義 #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x)) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x)) #define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");} #define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順 #define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順 #define repe(v, a) for(const auto& v : (a)) // a の全要素(変更不可能) #define repea(v, a) for(auto& v : (a)) // a の全要素(変更可能) #define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d ビット全探索(昇順) #define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て(昇順) #define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 #define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定 // 汎用関数の定義 template inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す) template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す) template inline T get(T set, int i) { return (set >> i) & T(1); } // 演算子オーバーロード template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repea(x, v) is >> x; return is; } template inline vector& operator--(vector& v) { repea(x, v) --x; return v; } template inline vector& operator++(vector& v) { repea(x, v) ++x; return v; } #endif // 折りたたみ用 #if __has_include() #include using namespace atcoder; #ifdef _MSC_VER #include "localACL.hpp" #endif //using mint = modint1000000007; //using mint = modint998244353; using mint = modint; // mint::set_mod(m); namespace atcoder { inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; } } using vm = vector; using vvm = vector; using vvvm = vector; using vvvvm = vector; #endif #ifdef _MSC_VER // 手元環境(Visual Studio) #include "local.hpp" #else // 提出用(gcc) inline int popcount(int n) { return __builtin_popcount(n); } inline int popcount(ll n) { return __builtin_popcountll(n); } inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; } inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; } inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; } inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; } #define gcd __gcd #define dump(...) #define dumpel(v) #define dump_list(v) #define dump_mat(v) #define input_from_file(f) #define output_to_file(f) #define Assert(b) { if (!(b)) while (1) cout << "OLE"; } #endif //【1 の連の長さ】O(n) /* * ビット列 s[0..n) について,'0' で区切られた '1' の連の長さを順に並べた列を返す. */ vi length1(const string& s, char one = '1') { // verify : https://atcoder.jp/contests/agc046/tasks/agc046_c vi len; int l = 0; repe(c, s) { if (c == one) { l++; } else { len.push_back(l); l = 0; } } len.push_back(l); len.erase(len.begin()); return len; } void shrink(vi& a) { int i = 0; while (i < sz(a) - 1) { if (a[i] < a[i + 1]) { a.erase(a.begin() + i); if (i > 0) i--; } else { i++; } } } vi to_seq(string s) { if (s == "0") s = ""; vi a = length1(s, '0'); // dump(a); shrink(a); // dump(a); return a; } void zikken() { rep(i, 16) { string s = bitset<10>(i).to_string(); while (!s.empty() && s[0] == '0') s.erase(s.begin()); auto a = to_seq(s); dump(i, "\t:", s, "\t:", length1(s, '0'), "\t\t:", a); } exit(0); } /* 0 : : : 1 : 1 : 0 : 0 2 : 10 : 1 : 1 3 : 11 : 0 0 : 0 0 4 : 100 : 2 : 2 5 : 101 : 1 0 : 1 0 6 : 110 : 0 1 : 1 7 : 111 : 0 0 0 : 0 0 0 8 : 1000 : 3 : 3 9 : 1001 : 2 0 : 2 0 10 : 1010 : 1 1 : 1 1 11 : 1011 : 1 0 0 : 1 0 0 12 : 1100 : 0 2 : 2 13 : 1101 : 0 1 0 : 1 0 14 : 1110 : 0 0 1 : 1 15 : 1111 : 0 0 0 0 : 0 0 0 0 */ struct S { // ω^e[0] + ω^e[1] + ... + ω^e[n-1] vector e; S() {} bool operator==(const S& g) const { return e == g.e; } bool operator!=(const S& g) const { return e != g.e; } bool operator<(const S& g) const { int n = sz(e), n2 = sz(g.e); repi(i, 0, max(n, n2)) { if (i == n && i == n2) return false; if (i == n) return true; if (i == n2) return false; if (e[i] == g.e[i]) continue; return e[i] < g.e[i]; } return false; } void add(const S& s) { while (!e.empty()) { if (e.back() < s) e.pop_back(); else break; } e.push_back(s); } #ifdef _MSC_VER friend ostream& operator<<(ostream& os, const S& f) { os << "("; repe(x, f.e) os << x; os << ")"; return os; } #endif }; void zikken2() { int N = 10; vector dp(N); dp[0] = S(); repi(n, 1, N - 1) { int n1 = lsb(n); int n0 = n >> (n1 + 1); // dump(n, n0, n1); dp[n] = dp[n0]; dp[n].add(dp[n1]); } dumpel(dp); rep(i, N) { rep(j, N) cout << (dp[i] < dp[j]) << " "; cout << endl; } exit(0); } /* 0: () 0 1: (()) 1 2: ((())) ω 3: (()()) 2 4: (((()))) ω^ω 5: ((())()) ω+1 6: (()(())) ω 7: (()()()) 3 8: ((()())) ω^2 9: (((()))()) ω^ω+1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 */ int main() { // input_from_file("input.txt"); // output_to_file("output.txt"); // zikken2(); // f(0) = 0 // f(1) = f(0) + ω^f(0) = 0 + ω^0 = 0 + 1 = 1 // f(2) = f(0) + ω^f(1) = 0 + ω^1 * 1 = ω // f(3) = f(1) + ω^f(0) = 1 + ω^0 = 1 + 1 = 2 // f(4) = f(0) + ω^f(2) = 0 + ω^ω = ω^ω // f(5) = f(2) + ω^f(0) = ω + ω^0 = ω + 1 // f(6) = f(1) + ω^f(1) = 1 + ω^1 = 1 + ω = ω // f(7) = f(3) + ω^f(0) = 2 + ω^0 = 3 // f(8) = f(0) + ω^f(3) = 0 + ω^2 = ω^2 // 0 : 0 [] // 1 : 1 [1] // 10 : ω [0,1] // 11 : 2 [2] // 100 : ω^ω [0,0,1] // 101 : ω + 1 [1,1] // 110 : ω [0,1] // 111 : 3 [3] // 1000 : ω^2 [???] // 1001 : ω^ω + 1 [1,0,1] int N = 100000; dump(N = 10); vector dp(N); dp[0] = S(); repi(n, 1, N - 1) { int n1 = lsb(n); int n0 = n >> (n1 + 1); dp[n] = dp[n0]; dp[n].add(dp[n1]); } dumpel(dp); string s, t; cin >> s >> t; vi a = length1(s, '0'); vi b = length1(t, '0'); dump(a); dump(b); S x, y; repe(l, a) x.add(dp[l]); repe(l, b) y.add(dp[l]); Yes(x < y); }