//#pragma GCC target("avx2") //#pragma GCC optimize("O3") //#pragma GCC optimize("unroll-loops") #include using namespace std; using ll = long long; using pii = pair; using pll = pair; using pli = pair; #define MOD 998244353 //#define MOD 1000000007 #define el '\n' #define El '\n' #define YESNO(x) ((x) ? "Yes" : "No") #define YES YESNO(true) #define NO YESNO(false) #define EXIT_ANS(x) {cout << (x) << '\n'; return;} #define PA() {EXIT_ANS(ans);} template void inline SORT(vector &v){sort(v.begin(),v.end()); return;} template void inline REV(vector &v){reverse(v.begin(),v.end()); return;} template void inline VEC_UNIQ(vector &v){sort(v.begin(),v.end()); v.erase(unique(v.begin(),v.end()),v.end()); return;} template T inline MAX(vector &v){return *max_element(v.begin(),v.end());} template T inline MIN(vector &v){return *min_element(v.begin(),v.end());} template T inline SUM(vector &v){T ans = 0; for(int i = 0; i < (int)v.size(); i++)ans += v[i]; return ans;} template void inline DEC(vector &v){for(int i = 0; i < (int)v.size(); i++)v[i]--; return;} template void inline INC(vector &v){for(int i = 0; i < (int)v.size(); i++)v[i]++; return;} void inline TEST(void){cerr << "TEST" << endl; return;} template bool inline chmin(T &x,T y){ if(x > y){ x = y; return true; } return false; } template bool inline chmax(T &x,T y){ if(x < y){ x = y; return true; } return false; } template vector inline get_vec(int n){ vector ans(n); for(int i = 0; i < n; i++)cin >> ans[i]; return ans; } template void inline print_vec(vector &vec,bool kaigyou = false){ int n = (int)vec.size(); for(int i = 0; i < n; i++){ cout << vec[i]; if(kaigyou || i == n - 1)cout << '\n'; else cout << ' '; } if(!n)cout << '\n'; return; } template void inline debug_vec(vector &vec,bool kaigyou = false){ int n = (int)vec.size(); for(int i = 0; i < n; i++){ cerr << vec[i]; if(kaigyou || i == n - 1)cerr << '\n'; else cerr << ' '; } if(!n)cerr << '\n'; return; } vector v; //[l1,r1] から一つ、[l2,r2] から一つ選んで、 xor の最小値はいくつになるか ll func(ll l1,ll r1,ll l2,ll r2){ if(l1 <= l2 && l2 <= r1)return 0; if(l1 <= r2 && r2 <= r1)return 0; if(l2 < r1){ swap(l1,l2); swap(r1,r2); } //cerr << l1 << ' ' << r1 << ' ' << l2 << ' ' << r2 << ' '; //l1 <= r1 < l2 <= r2 assert(l1 == 0); assert(r1 < l2); ll ans = 0; for(int i = 37; i >= 0; i--){ if(!(r2 & (1LL << i)))continue; if(r1 & (1LL << i)){ ans += func(0,r1 - (1LL << i),l2 - (1LL << i),r2 - (1LL << i)); return ans; } if(l2 & (1LL << i)){ l2 -= (1LL << i); r2 -= (1LL << i); ans += (1LL << i); if(r1 >= l2){ //cerr << ans << el; return ans; } continue; } r2 = (1LL << i) - 1; continue; } //cerr << ans << el; return ans; } ll saiki(ll l,ll r){ //cerr << l << ' ' << r << el; if(l == r)return 0; if(r == l + 1)return (l ^ r); int k = -1; for(int i = 37; i >= 0; i--){ bool bl = (((1LL << i) & l) != 0); bool br = (((1LL << i) & r) != 0); if(bl == br){ if(bl){ l -= (1LL << i); r -= (1LL << i); } continue; } k = i; break; } assert(k != -1); if(l == 0 && r == (1LL << (k + 1)) - 1){ return v[k]; } ll ans = saiki(l,(1LL << k) - 1); ans += saiki((1LL << k),r); //if(r - l >= (1LL << k))return (ans + (1LL << k)); //[l,(1LL << k)-1], [(1LL << k),r] から1個ずつ値を選ぶとして、 xor の最小値はいくつか? //[0,r - (1LL << k)] //[l,(1LL << k)-1] から1個ずつ値を選ぶとして、 xor の最小値はいくつか?に ans + (1LL << k) を足せばよい //l で上から抑えられるが、もっと小さいのもあるしあんまり意味はない? ans += (1LL << k); //cerr << 0 << ' ' << r - (1LL << k) << ' ' << l << ' ' << (1LL << k) - 1 << ' ' << func(0,r - (1LL << k),l,(1LL << k) - 1,33) << el; ans += func(0,r - (1LL << k),l,(1LL << k) - 1); return ans; } #define MULTI_TEST_CASE true void solve(void){ //問題を見たらまず「この問題設定から言えること」をいっぱい言う //よりシンプルな問題に言い換えられたら、言い換えた先の問題を自然言語ではっきりと書く //複数の解法のアイデアを思いついた時は全部メモしておく //g++ -D_GLIBCXX_DEBUG -Wall -O2 e.cpp -o o //クラスカル法の気持ちになろう //2k,2k+1 は真っ先に繋いで良い(1) //次に、4k,4k+2(or 4k+1,4k+3) を繋ぎたい(2) //次に、8k,8k+4(or 8k+1,8k+5 or 8k+2,8k+6 or 8k+3,8k+7) を繋ぎたい(4) //こういう感じで logN くらいでやるしかないよなあ long long n,m; cin >> n >> m; //cerr << saiki(n,m) << el; return; cout << (long long)saiki(m,m + n - 1) << el; return; } void calc(void){ v.push_back(1); for(int i = 1; i < 40; i++){ v.push_back(v.back() * 2LL + (1LL << i)); } return; } signed main(void){ cin.tie(nullptr); ios::sync_with_stdio(false); calc(); int t = 1; if(MULTI_TEST_CASE)cin >> t; while(t--){ solve(); } return 0; }