// clang-format off #include using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; using pii = pair; using pll = pair; template using vec = vector; template using vvec = vector>; #define rep(i, n) for (int i = 0; i < (n); i++) #define rrep(i, n) for (int i = int(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) constexpr char ln = '\n'; template inline int SZ(const Container& v) { return int(v.size()); } template inline void UNIQUE(vector& v) { v.erase(unique(v.begin(), v.end()), v.end()); } template inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; } inline int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); } inline int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); } inline int popcount(ull x) { return __builtin_popcountll(x); } inline int kthbit(ull x, int k) { return (x >> k) & 1; } inline constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x - 1) * 10; } const string YESNO[2] = {"NO", "YES"}; const string YesNo[2] = {"No", "Yes"}; inline void YES(bool t = true) { cout << YESNO[t] << "\n"; } inline void Yes(bool t = true) { cout << YesNo[t] << "\n"; } template inline void drop(T x) { cout << x << "\n"; exit(0); } inline void print() { cout << "\n"; } template inline void print(const vector& v) { for (auto it = v.begin(); it != v.end(); ++it) { if (it != v.begin()) { cout << " "; } cout << *it; } print(); } template inline void print(const T& x, const Args& ... args) { cout << x << " "; print(args...); } #ifdef MINATO_LOCAL template ostream& operator<<(ostream& os, pair p) { return os << "(" << p.first << ", " << p.second << ")"; } template void debug_tuple(ostream& os, TUPLE _) { (void)os; (void)_; } template void debug_tuple(ostream &os, TUPLE t) { os << (N == 0 ? "" : ", ") << get(t); debug_tuple(os, t); } template ostream& operator<<(ostream& os, tuple t) { os << "("; debug_tuple<0, tuple, Args...>(os, t); return os << ")"; } string debug_delim(int& i) { return i++ == 0 ? "" : ", "; } #define debug_embrace(x) { int i = 0; os << "{"; { x } return os << "}"; } template ostream& operator<<(ostream& os, vector v) { debug_embrace( for (T e : v) { os << debug_delim(i) << e; } ) } template ostream& operator<<(ostream& os, array a) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) } template enable_if_t>, ostream>& operator<<(ostream& os, T(&a)[N]) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) } template ostream& operator<<(ostream& os, set s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) } template ostream& operator<<(ostream& os, map mp) { debug_embrace( for (auto e : mp) { os << debug_delim(i) << e; }) } template ostream& operator<<(ostream& os, multiset s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) } template ostream& operator<<(ostream& os, queue q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.front(); } ) } template ostream& operator<<(ostream& os, deque q) { debug_embrace( for (T e : q) { os << debug_delim(i) << e; } ) } template ostream& operator<<(ostream& os, priority_queue q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) } template ostream& operator<<(ostream& os, priority_queue, greater> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) } void debug_out() { cerr << endl; } template void debug_out(const T& x, const Args& ... args) { cerr << " " << x; debug_out(args...); } #define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__) #else #define debug(...) (void(0)) #endif struct fast_ios { fast_ios() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); cerr << fixed << setprecision(7); }; } fast_ios_; /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// // clang-format on using Ans = tuple; int main() { int N, K; cin >> N >> K; int tmp = N; // [l,r) int memory_l = 0; int memory_r = N; int BIT_SIZE = topbit(N); vec ans; auto UPD = [&](int i, int x) { assert(0 <= i and i <= N); assert(x == 0 or x == 1); ans.emplace_back("UPD", i, x, -1); return; }; auto AND = [&](int i, int j, int k) { assert(0 <= i and i <= N); assert(0 <= j and j <= N); assert(0 <= k and k <= N); ans.emplace_back("AND", i, j, k); }; auto XOR = [&](int i, int j, int k) { assert(0 <= i and i <= N); assert(0 <= j and j <= N); assert(0 <= k and k <= N); ans.emplace_back("XOR", i, j, k); }; auto ANS = [&]() { cout << ans.size() << ln; for (auto& [str, i, j, k] : ans) { cout << str << " " << i << " " << j; if (~k) cout << " " << k; cout << ln; } }; auto dbg = [&]() { ans.emplace_back("DBG", -1, -1, -1); }; auto SWAP = [&](int i, int j) { assert(0 <= i and i <= N); assert(0 <= j and j <= N); if (i == j) return; XOR(i, i, j); // x^y,y XOR(j, i, j); // x^y,x XOR(i, i, j); // y,x return; }; auto compress = [&]() { int xor_l = memory_l; int xor_r = memory_r; int and_l = memory_l; int and_r = and_l; while (xor_r - xor_l > 1) { int cnt = (xor_r - xor_l) / 2; rep(c, cnt) { int i = xor_l + c * 2; int j = xor_l + c * 2 + 1; XOR(tmp, i, j); AND(i, i, j); SWAP(j, tmp); UPD(tmp, 0); } { int and_pos = xor_l + cnt; if (cnt & 1) and_pos++; int xor_pos = xor_l + 1; rep(k, cnt / 2) { SWAP(and_pos, xor_pos); and_pos += 2; xor_pos += 2; } } and_r += cnt; xor_l += cnt; // dbg(); } SWAP(xor_l, tmp); UPD(xor_l, 0); tmp--; memory_l = and_l; memory_r = and_r; }; auto sub = [&](int k, int cnt) { XOR(cnt, cnt, k); AND(cnt, cnt, k); UPD(k, 0); return; }; auto carry_down = [&](int carry, int cnt) { XOR(cnt, carry, cnt); AND(carry, cnt, carry); return; }; auto solve = [&]() { // dbg(); rep(k, BIT_SIZE + 1) { compress(); // dbg(); } int k = memory_l; int cnt = N; UPD(k, K & 1); sub(k, cnt); rep(b, BIT_SIZE) { int carry = cnt; cnt--; carry_down(carry, cnt); UPD(k, kthbit(K, b + 1)); sub(k, cnt); XOR(cnt, cnt, carry); } SWAP(cnt, N); UPD(0, 1); XOR(N, 0, N); }; solve(); ANS(); auto test = [&]() { debug(BIT_SIZE); int Q; cin >> Q; rep(_, Q) { vec A(N + 1); rep(i, N) cin >> A[i]; int S = accumulate(all(A), 0); auto B = A; for (auto& [str, i, j, k] : ans) { if (str == "UPD") { B[i] = j; } else if (str == "AND") { B[i] = B[j] & B[k]; } else if (str == "XOR") { B[i] = B[j] ^ B[k]; } else if (str == "DBG") { debug(B); } } if ((S >= K) ^ B[N]) { debug(B); } } }; // test(); }