#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 vl = vector; using vvl = vector; using vvvl = 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 = 4004004004004004004LL; double EPS = 1e-12; // 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 // 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) // 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; } // 手元環境(Visual Studio) #ifdef _MSC_VER #include "local.hpp" // 提出用(gcc) #else 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 input_from_file(f) #define output_to_file(f) #define Assert(b) { if (!(b)) while (1) cout << "OLE"; } #endif #endif // 折りたたみ用 //--------------AtCoder 専用-------------- #include using namespace atcoder; using mint = modint1000000007; //using mint = modint998244353; //using mint = modint; // mint::set_mod(m); istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; } using vm = vector; using vvm = vector; using vvvm = vector; //---------------------------------------- //【局面のニム値】O(?)(遅いので実験用) /* * 初期局面 p から遷移可能な局面とそのニム値のリストを nim に格納する. * nxt(p, nps) を呼ぶと,p から遷移可能な局面のリストを nps に格納するものとする. */ template void calc_nimber(const T& p, function&)>& nxt, map& nim) { nim.clear(); function calc_nimber = [&](const T& p) { if (nim.count(p)) return nim[p]; vector nps; nxt(p, nps); vi next_nimbers; repe(np, nps) { next_nimbers.push_back(calc_nimber(np)); } uniq(next_nimbers); int i = 0; while (i < sz(next_nimbers) && next_nimbers[i] == i) i++; nim[p] = i; return nim[p]; }; calc_nimber(p); } void zikken() { using T = vi; function&)> nxt = [&](const T& p, vector& nps) { rep(i, sz(p)) { if (p[i] == 1) continue; if ((i == 0 || p[i - 1] == 1) && (i == sz(p) - 1 || p[i + 1] == 1)) { T np(p); np[i] = 1; nps.push_back(np); } } repi(i, 1, sz(p) - 2) { if (p[i - 1] == 1 || p[i] == 1 || p[i + 1] == 1) continue; T np1(p); np1[i] = np1[i - 1] = 1; nps.push_back(np1); T np2(p); np2[i] = np2[i + 1] = 1; nps.push_back(np2); } }; repi(n, 0, 25) { T p(n + 1); p[0] = 1; map nim; calc_nimber(p, nxt, nim); dump(n, nim[p]); } exit(0); repi(n, 0, 25) { T p(n + 2); p[0] = p[n + 1] = 1; map nim; calc_nimber(p, nxt, nim); dump(n, nim[p]); } exit(0); } /* 片側の開いた長さ i の '0' の連 0 0 1 1 2 0 3 0 4 1 5 2 6 2 7 1 8 4 9 0 10 1 11 4 12 2 13 1 14 4 15 0 16 1 17 4 18 2 19 1 20 4 21 2 22 1 23 0 24 2 25 1 両側とも閉じた長さ i の '0' の連 0 0 1 1 2 0 3 0 4 1 5 2 6 2 7 1 8 4 9 0 10 1 11 4 12 2 13 1 14 4 15 0 16 1 17 4 18 2 19 1 20 4 21 2 22 1 23 0 24 2 25 1 http://oeis.org/A071430 Sprague-Grundy values for octal game .16 山から 1 つの石を取り除く場合,残る山の数を 0 にすることができる. 山から 2 つの石を取り除く場合,残る山の数を 1 または 2 にすることができる. Sequence is eventually periodic with period 149459. The last exception is at n=105350. */ string TLE(int n, ll k, vl a) { a.insert(a.begin(), 0); a.push_back(k + 1); chmax(k, 10LL); vi dp(k + 1); dp[0] = 0; dp[1] = 1; dp[2] = 0; repi(i, 3, k) { int set = 0; repi(j, 0, (i - 2) / 2) { set |= 1 << (dp[j] ^ dp[i - j - 2]); } dp[i] = lsb(~set); } dump(dp); int res = 0; rep(i, n + 1) { ll w = a[i + 1] - a[i] - 1; dump(w); res ^= dp[w]; } return res ? "Yes" : "No"; } //【ランレングス符号】O(n) /* * a[0..n) をランレングス符号化し,結果を cls に格納する. * cls[i] = {c, l} は前から i 番目の列が l 個の文字 c からなることを表す. */ template void run_length_encodeing(const vector& a, vector>& cls) { // verify : https://atcoder.jp/contests/arc024/tasks/arc024_2 int n = sz(a); cls.clear(); if (n == 0) return; cls.push_back({ a[0], 1 }); // 今読んでいる文字の種類を記憶する. T c = a[0]; repi(i, 1, n - 1) { // 記憶している文字と同じ文字の場合 if (c == a[i]) { // 列の長さを増やす. cls.rbegin()->second++; } // 記憶している文字と異なる文字の場合 else { // 新しい文字を記憶しておく. c = a[i]; // 新たな列を追加する. cls.push_back({ c, 1 }); } } } void umekomi() { auto start = chrono::system_clock::now(); int k = 149459 + 105350 + 10; k = k / 3 * 3; k = 10002; // デバッグ用 vi dp(k); dp[0] = 0; dp[1] = 1; dp[2] = 0; repi(i, 3, k - 1) { int set = 0; repi(j, 0, (i - 2) / 2) { set |= 1 << (dp[j] ^ dp[i - j - 2]); } dp[i] = lsb(~set); } dump(dp); rep(i, k) { if (14 <= dp[i] && dp[i] <= 17) dp[i] -= 4; else if (22 <= dp[i] && dp[i] <= 23) dp[i] -= 8; } vi dp3(k / 3); rep(i, k / 3) dp3[i] = ((dp[3 * i] * 16) + dp[3 * i + 1]) * 16 + dp[3 * i + 2]; // dump(dp3); vector cls; run_length_encodeing(dp3, cls); // dump(cls); cout << "string s = R\"("; repe(cl, cls) { int c, l; tie(c, l) = cl; char c1 = ':' + c / 64; char c2 = ':' + c % 64; cout << c1 << c2; if (l >= 2) cout << l; } cout << "~)\";" << endl; auto now = chrono::system_clock::now(); auto msec = chrono::duration_cast(now - start).count(); dump(msec); exit(0); } /* 24859 (25秒で終わった) */ const char* s = 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string solve(int n, ll k, vl a) { vi dp; int i = 0; while (s[i] != '~') { int c1 = s[i++] - ':'; int c2 = s[i++] - ':'; int c = c1 * 64 + c2; int l = 0; while (s[i] <= '9') l = l * 10 + s[i++] - '0'; if (l == 0) l = 1; int d0 = c / 16 / 16; int d1 = c / 16 % 16; int d2 = c % 16; rep(hoge, l) { dp.emplace_back(d0); dp.emplace_back(d1); dp.emplace_back(d2); } } // dump(dp); rep(i, sz(dp)) { if (14 - 4 <= dp[i] && dp[i] <= 17 - 4) dp[i] += 4; else if (22 - 8 <= dp[i] && dp[i] <= 23 - 8) dp[i] += 8; } // dump(dp); a.insert(a.begin(), 0); a.push_back(k + 1); int res = 0; rep(i, n + 1) { ll w = a[i + 1] - a[i] - 1; // dump(w); if (w >= sz(dp)) { w = (w - 105352) % 149459 + 105352; } res ^= dp[w]; } return res ? "Yes" : "No"; } int main() { // input_from_file("input.txt"); output_to_file("output.txt"); // umekomi(); int n; ll k; cin >> n >> k; vl a(n); cin >> a; cout << solve(n, k, a) << endl; }