Submission #66386734

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Source Code Expand

#include <string>
#include <vector>
#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<stack>
#include<queue>
#include<cmath>
#include<algorithm>
#include<functional>
#include<list>
#include<deque>
#include<bitset>
#include<set>
#include<map>
#include<unordered_map>
#include<unordered_set>
#include<cstring>
#include<sstream>
#include<complex>
#include<iomanip>
#include<numeric>
#include<cassert>
#include<random>
#define X first
#define Y second
#define pb push_back
#define rep(X,Y) for (int X = 0;X < (int)(Y);++X)
#define reps(X,S,Y) for (int X = (int)(S);X < (int)(Y);++X)
#define rrep(X,Y) for (int X = (int)(Y)-1;X >=0;--X)
#define rreps(X,S,Y) for (int X = (int)(Y)-1;X >= (int)(S);--X)
#define repe(X,Y) for (X = 0;X < (Y);++X)
#define peat(X,Y) for (;X < (Y);++X)
#define all(X) X.begin(),X.end()
#define rall(X) X.rbegin(),X.rend()
#define eb emplace_back
#define UNIQUE(X) X.erase(unique(all(X)),X.end())
#define Endl endl
#define NL <<"\n"
#define cauto const auto

using namespace std;
using ll=long long;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
template<class T> using vv=vector<vector<T>>;
template<class T> inline bool MX(T &l,const T &r){return l<r?l=r,1:0;}
template<class T> inline bool MN(T &l,const T &r){return l>r?l=r,1:0;}
//#undef NUIP
#ifdef NUIP
#include "benri.h"
#else
#define out(args...)
#endif
void ouT(ll x,int d=3){auto re=to_string(x);if((int)re.size()>d) re=x>0?"oo":"-oo";cout<<string(d-re.size(),' ')<<re<<",";}
#ifdef __cpp_init_captures
template<typename T>vector<T> table(int n, T v){ return vector<T>(n, v);}
template <class... Args> auto table(int n, Args... args){auto val = table(args...); return vector<decltype(val)>(n, move(val));}
#endif
template<class A,class B> pair<A,B> operator+(const pair<A,B> &p,const pair<A,B> &q){ return {p.X+q.X,p.Y+q.Y};}
template<class A,class B,class C,class D> pair<A,B>& operator+=(pair<A,B> &p,const pair<C,D> &q){ p.X+=q.X; p.Y+=q.Y; return p;}
template<class A,class B> pair<A,B> operator-(const pair<A,B> &p,const pair<A,B> &q){ return {p.X-q.X,p.Y-q.Y};}
template<class A,class B,class C,class D> pair<A,B>& operator-=(pair<A,B> &p,const pair<C,D> &q){ p.X-=q.X; p.Y-=q.Y; return p;}
template<class A,class B> istream& operator>>(istream &is, pair<A,B> &p){ is>>p.X>>p.Y; return is;}
#ifdef __cpp_init_captures
template<class Tuple, size_t... Is> void read_tuple_impl(istream &is, Tuple& t, index_sequence<Is...>){((is >> get<Is>(t)), ...);}
template<class... Args> auto& operator>>(istream &is, tuple<Args...>& t){ read_tuple_impl(is, t, index_sequence_for<Args...>{}); return is;}
template<typename T, size_t... Is> void addadd(T& t1, const T& t2, integer_sequence<size_t, Is...>){ cauto l = { (get<Is>(t1) += get<Is>(t2), 0)... }; (void)l;}
template <typename...T>tuple<T...>& operator += (tuple<T...>& lhs, const tuple<T...>& rhs){	addadd(lhs, rhs, index_sequence_for<T...>{});	return lhs;}
template <typename...T>tuple<T...> operator +(tuple<T...> lhs, const tuple<T...>& rhs){ return lhs += rhs;}
template<typename T, size_t... Is> void subsub(T& t1, const T& t2, integer_sequence<size_t, Is...>){ cauto l = { (get<Is>(t1) -= get<Is>(t2), 0)... }; (void)l;}
template <typename...T>tuple<T...>& operator -= (tuple<T...>& lhs, const tuple<T...>& rhs){	subsub(lhs, rhs, index_sequence_for<T...>{});	return lhs;}
template <typename...T>tuple<T...> operator - (tuple<T...> lhs, const tuple<T...>& rhs){ return lhs -= rhs;}
#endif
template<class T=ll> T read(){ T re; cin>>re; return re;}
template<class T=ll> T read(const T &dec){ T re; cin>>re; return re-dec;}
template<class T=ll> vector<T> readV(const int sz){ vector<T> re(sz); for(auto &x:re) x=read<T>(); return re;}
template<class T=ll> vector<T> readV(const int sz, const T &dec){ vector<T> re(sz); for(auto &x:re) x=read<T>(dec); return re;}
vv<int> readG(const int &n,const int &m){ vv<int> g(n); rep(_,m){ cauto a=read<int>(1),b=read<int>(1); g[a].pb(b); g[b].pb(a);} return g;}
vv<int> readG(const int &n){ return readG(n,n-1);}
vv<int> readD(const int &n,const int &m){ vv<int> g(n); rep(_,m){ cauto a=read<int>(1),b=read<int>(1); g[a].pb(b); } return g;}
vv<int> readD(const int &n){ return readD(n,n-1);}
template<class T> vv<pair<int,T>> readG(const int &n,const int &m){ vv<pair<int,T>> g(n); rep(_,m){ cauto a=read<int>(1),b=read<int>(1); cauto c=read<T>(); g[a].eb(b,c); g[b].eb(a,c);} return g;}
template<class T> vv<pair<int,T>> readG(const int &n){ return readG<T>(n,n-1);}
template<class T> vv<pair<int,T>> readD(const int &n,const int &m){ vv<pair<int,T>> g(n); rep(_,m){ cauto a=read<int>(1),b=read<int>(1); cauto c=read<T>(); g[a].eb(b,c); } return g;}
template<class T> vv<pair<int,T>> readD(const int &n){ return readD<T>(n,n-1);}
#ifdef __cpp_deduction_guides
template<typename T> vector<T> readT(int n, T v){ return readV(n,v);}
template <class... Args> auto readT(int n, Args... args){ vector re(1,readT(args...));rep(_,n-1) re.eb(readT(args...));	return re;}
#endif
template<class T> bool erase(multiset<T> &st, const T &v){if(cauto it=st.find(v); it==st.end()) return false; else{ st.erase(it); return true;}}
#ifdef NUIP
#define TT cauto TTT=read();rep(kase,TTT)if(cerr<<"Case #"<<kase<<endl)
#else
#define TT cauto TTT=read();rep(kase,TTT)
#endif
struct sorted_impl{template<class T>friend vector<T>operator-(vector<T>a,sorted_impl){sort(all(a));return a;}friend string operator-(string a,sorted_impl){sort(all(a));return a;}}sorted;struct reversed_impl{template<class T>friend vector<T>operator-(vector<T> a,reversed_impl){reverse(all(a));return a;}friend string operator-(string a,reversed_impl){reverse(all(a));return a;}}reversed;struct distinct_impl{template<class T>friend vector<T>operator-(vector<T> a,distinct_impl){sort(all(a));UNIQUE(a);return a;}}distinct;template<class S>struct sortedWith{const S f;sortedWith(const S &f):f(f){}template<class T>friend vector<T>operator-(vector<T> a,const sortedWith&b){sort(all(a),[&](cauto&i,cauto&j){return b.f(i)<b.f(j);});return a;}};
template<class T>int operator/(const T&v,const vector<T>&vs){return lower_bound(all(vs),v)-vs.begin();}
vector<int> Inds(const int n){vector<int> inds(n);iota(all(inds),0);return inds;}
const ll MOD=1e9+7; //998244353;

vector<int> solve(const ll goal, const int n, const int dig){
	vector<ll> cur(n);
	rep(i,n) cur[i]=1ll<<i;
	vector<int> re;
	cauto swp=
		[&](const int i){
			re.eb(i);
			cur[i]=cur[i+1]^=cur[i];
		};
	if(goal>>dig&1){
		swp(dig);
	}else{
		swp(dig);
		swp(dig);
	}
	//out(re,cur,1);
	int i=dig;
	for(;i+2<n;++i){
		if(goal>>(i+2)&1){
			swp(i+1);
			swp(i); swp(i);
			swp(i+1);
		}else{
			swp(i+1); swp(i+1);
			swp(i); swp(i+1);
			swp(i); swp(i+1);
		}
	}
	//out(re,cur,1);
	for(;i;--i){
		if(goal>>(i-1)&1){
			swp(i-1);
			swp(i); swp(i);
			swp(i-1);
		}else{
			swp(i-1); swp(i-1);
			swp(i); swp(i-1);
			swp(i);
			swp(i-1);
		}
	}
	if(cur[0]!=goal){
	// 	out(goal,n,dig,re,cur,1);
	// 	exit(0);
	// }
	// if(cur[0]!=goal,0){
		rep(_,MOD) cout<<string(MOD,'1');
		cout NL;
	}
	return re;
}

int main(){
	ios_base::sync_with_stdio(false); cin.tie(0);
	cout<<fixed<<setprecision(0);

	// reps(n,3,20){
	// 	rep(goal,1<<n){
	// 		int dig=-1;
	// 		rep(i,n-1)if(cauto b=goal>>i&3; b==0 || b==3){ dig=i; break;}
	// 		if(dig<0) continue;
	// 		solve(goal,n,dig);
	// 	}
	// 	out(n,1);
	// }
	// return 0;

	
	TT{
		cauto n=read(0);
		cauto t=read();
		cauto vs=readV(n);
		vector<pll> bss(60);
		ll zero=0;
		rep(i,n){
			ll cur=vs[i];
			ll st=1ll<<i;
			rep(d,60)if(bss[d].X && (cur>>d&1)){
				cur^=bss[d].X;
				st^=bss[d].Y;
			}
			if(cur==0){
				if(st+1!=(1ll<<n)) zero=st;
				continue;
			}
			cauto ind=__builtin_ctzll(cur);
			rep(d,60)if(d!=ind && (bss[d].X>>ind&1)){
				bss[d].X^=cur;
				bss[d].Y^=st;
			}
			bss[ind]=pll(cur,st);
		}
		ll goal=0;
		{
			ll cur=t;
			rep(d,60)if(bss[d].X && (cur>>d&1)){
				cur^=bss[d].X;
				goal^=bss[d].Y;
			}
			if(cur){
				cout<<"No" NL;
				continue;
			}
		}
		int dig=-1;
		rep(i,n-1)if(cauto b=goal>>i&3; b==0 || b==3){ dig=i; break;}
		out(n,t,vs,bss,goal,1);
		vector<int> re;
		if(dig>=0){
			re=solve(goal,n,dig);
		}else if(zero){
			goal^=zero;
			rep(i,n-1)if(cauto b=goal>>i&3; b==0 || b==3){ dig=i; break;}
			re=solve(goal,n,dig);
		}else{
			cout<<"No" NL;
			continue;
		}
		{
			vector<ll> cur=vs;
			for(cauto &i:re) cur[i]=cur[i+1]^=cur[i];
			assert(cur[0]==t);
		}
		cout<<"Yes" NL;
		cout<<re.size() NL;
		for(cauto &v:re) cout<<v+1<<" ";
		cout NL;
	}
	
	if(0)reps(n,3,20){
		out(n,1);
		vector<int> vs(n);
		rep(i,n) vs[i]|=1<<i;
		queue<vector<int>> que;
		set<vector<int>> st;
		map<vector<int>,vector<int>> prv;
		st.emplace(vs); que.emplace(vs);
		while(que.size()){
			cauto vs=que.front(); que.pop();
			reps(i,1,n){
				auto us=vs;
				us[i]^=us[i-1];
				us[i-1]=us[i];
				if(st.emplace(us).Y){
					que.emplace(us);
					prv.emplace(us,vs);
				}
			}
		}
		// for(cauto &vs:st)if(vs[0]==0b0110){
		// 		out(vs,1);
		// 		for(auto us=vs; us.size(); us=prv[us]) out(us,1);
		// 		break;
		// 	}
		set<int> re;
		for(cauto &vs:st) re.emplace(vs[0]);
		rep(st,1<<n){
			bool ok=false;
			rep(i,n-1)if(cauto b=st>>i&3; b==0 || b==3) ok=true;
			if(ok!=re.count(st)){
				out(st,1);
				rep(d,n) cout<<(st>>d&1);
				cout NL;
				break;
			}
		}
		// for(cauto v:re){
		// 	rep(d,n) cout<<(v>>d&1);
		// 	cout NL;
		// }
	}
	return 0;
}

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