This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include "bits/stdc++.h"
using namespace std;
#define FAST ios_base::sync_with_stdio(false); cin.tie(0);
#define pb push_back
#define eb emplace_back
#define ins insert
#define ph push
#define f first
#define s second
#define cbr cerr << "hi\n"
#define mmst(x, v) memset((x), v, sizeof ((x)))
#define siz(x) ll(x.size())
#define all(x) (x).begin(), (x).end()
#define lbd(x, y) lower_bound(all(x), y)
#define ubd(x, y) upper_bound(all(x), y)
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); //can be used by calling rng() or shuffle(A, A+n, rng)
inline long long rand(long long x, long long y) { return (rng() % (y+1-x)) + x; } //inclusivesss
string inline to_string(char c) {string s(1,c);return s;} template<typename T> inline T gcd(T a,T b){ return a==0?llabs(b):gcd(b%a,a); }
typedef long long ll;
typedef long double ld;
#define FOR(i,s,e) for(ll i=s;i<=ll(e);++i)
#define DEC(i,s,e) for(ll i=s;i>=ll(e);--i)
typedef pair<ll,ll>pi; typedef pair<ll,pi>spi; typedef pair<pi,pi>dpi;
#define LLINF ((long long)1e18)
#define INF int(1e9+1e6)
#define MAXN (300006)
bool state[MAXN];
void solve(){
mmst(state,0);
ll n,q;cin>>n>>q;
FOR(i,0,q-1){
ll a; cin>>a;
state[a]=1;
}
vector<ll> comp;
vector<vector<bool>> dp(2,vector<bool>(n+4,0));
vector<ll> moves, ans, re;
auto gogo=[&](){
if(comp.empty())return 1;
vector<vector<ll>> came(siz(comp), vector<ll>());
FOR(i,0,siz(comp)-1){
came[i].resize(comp[i]+3);
FOR(j,0,comp[i]+2) dp[i&1][j]=0, came[i][j]=-1;
if(i) for(ll j=1;j<=min(comp[i-1],comp[i]);++j) if(dp[(i-1)&1][j]) {
dp[i&1][comp[i]-j]=1, came[i][comp[i]-j]=j;
}
if(comp[i]>2){
DEC(j,comp[i]-1,0){
if(dp[i&1][j+2]&&!dp[i&1][j]){
came[i][j]=came[i][j+2];
}
dp[i&1][j]=dp[i&1][j]|dp[i&1][j+2];
}
}
if(i==0||dp[(i-1)&1][0]){
dp[i&1][comp[i]]=1, came[i][comp[i]]=0;
DEC(j,comp[i]-1,1){
if(dp[i&1][j+2]&&!dp[i&1][j]){
came[i][j]=came[i][j+2];
}
dp[i&1][j]=dp[i&1][j]|dp[i&1][j+2];
}
}
}
if(dp[(siz(comp)-1)&1][0]){
ll x=siz(comp)-1, y=0;
assert(moves.empty());
moves.pb(0);
while(x){
assert(~came[x][y]), moves.pb(came[x][y]), y=came[x][y], -- x;
}
reverse(all(moves));
assert(moves.size()==comp.size());
re.clear(), re.resize(moves.size(),0);
FOR(i,0,siz(moves)-1){
if(i==0) {
re[i]=moves[i], moves[i]=comp[i]-moves[i];
}else{
re[i]=moves[i], moves[i]=comp[i]-re[i-1]-moves[i];
}
}
return 1;
}
cout<<"-1\n";
return 0;
};
ll past=0;
auto get_move=[&](){
assert(moves.size()==comp.size());
ll opast=past;
FOR(i,0,siz(comp)-1){
ll to_bye=moves[i];
assert(to_bye%2==0);
to_bye/=2;
assert(comp[i]-to_bye*2>=1); assert(comp[i]-to_bye*2-(i?re[i-1]:0)==re[i]);
while(to_bye--){
ans.pb(past+2);assert(state[past+2]==0);
}
past += comp[i] + 1;
}
past=opast;
FOR(i,0,siz(comp)-1){
past+=comp[i]+1;
moves[i]=re[i];
if(siz(comp)-1==i)assert(moves[i]==0);
while(moves[i]--)assert(state[past]==1),ans.pb(past);
}
};
FOR(i,1,n){
if(state[i]==0){
if(i>1&&state[i-1]==0) {
++ comp.back();
}else{
comp.pb(1);
}
}else{
if(i>1&&state[i-1]==1){
if(!gogo())return;
get_move();
comp.clear();
moves.clear(), re.clear();
++ past;
}else { past+=(i==1); assert(i==1||comp.size()); }
}
}
if(!gogo())return;
get_move();
if(state[n]==0)assert(past==n+1);
else assert(past==n);
cout<<ans.size()<<'\n';
for(auto i:ans)assert(i>1&&i<n),cout<<i<<' ';cout<<'\n';
}
int main(){
FAST
ll t; cin>>t;
while(t--)solve();
}
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