#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 using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef long double ld; typedef pair LDP; const ld eps = 1e-8; const ld pi = acosl(-1.0); ll mod_pow(ll x, ll n, ll m = mod) { if (x >= m)x %= m; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n % mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } const int max_n = 1 << 19; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } ll gcd(ll a, ll b) { if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } bool is2n(int x) { while (x % 2 == 0)x /= 2; return x == 1; } bool add(vector& v, int x) { rep(i, v.size()) { per(j, 20) { bool bl = v[i] & (1 << j); bool br = x & (1 << j); if (bl && br) { x ^= v[i]; break; } else if (bl) { break; } else if (br) { v.insert(v.begin() + i, x); return false; } } } if (x == 0)return true; v.push_back(x); return false; } void solve() { int k, x; cin >> k >> x; if (x == 0) { cout << "Yes\n"; cout << 1 << "\n"; cout << (k ^ 1) << "\n"; return; } if (k == 0) { x++; } if (!is2n(x)) { cout << "No\n"; return; } vectorans; ans.push_back(k); vector v; v.push_back(k); int z = 1; if (k == 0)z = 2; rep(i, 1 << 20) { if (z == x)break; ans.push_back(i); if (add(v, i))z *= 2; /*cout << "hoge"< 0)cout << " "; cout << ans[i]; } cout << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(15); //init_f(); //init(); //expr(); //int t; cin >> t; rep(i, t) solve(); return 0; }