/* Problem URL: https://codeforces.com/problemset/problem/1868/B1 */ #include #include #include using namespace std; using namespace __gnu_pbds; template > using ordered_set = tree; #define V vector #define rmin(a, b) a = min(a, b) #define rmax(a, b) a = max(a, b) #define rep(i, lim) for (int i = 0; i < (lim); i++) #define nrep(i, s, lim) for (int i = s; i < (lim); i++) #define repv(i, v) for (auto &i : (v)) #define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; } #define sortv(v) sort(v.begin(), v.end()) #define all(v) (v).begin(), (v).end() using vi = vector; using vvi = vector; using vvvi = vector; using vvvvi = vector; using ll = long long; using vl = vector; using vvl = vector; using vvvl = vector; using vvvvl = vector; template auto operator<<(ostream &os, const vector &vec)->ostream& { os << vec[0]; for (size_t i = 1; i < vec.size(); i++) { os << ' ' << vec[i]; } os << '\n'; return os; } template auto operator>>(istream &is, vector &vec)->istream& { for (auto &i : vec) { is >> i; } return is; } template auto operator<<(ostream &os, const vector> &vec)->ostream& { for (auto &i : vec) { os << i[0]; for (size_t j = 1; j < i.size(); j++) { os << ' ' << i[j]; } os << '\n'; } return os; } template auto operator>>(istream &is, vector> &vec)->istream& { for (auto &i : vec) { for (auto &j : i) { is >> j; } } return is; } const int oo = INT32_MAX >> 1; const ll OO = INT64_MAX >> 1; void pre() { } #define TEST 1 void solve() { int n; cin >> n; vi a(n); ll total = 0; repv(i, a) { cin >> i; total += i; } if (total % n) { cout << "No\n"; return; } total /= n; vi rem(32); vi add(32); int wild = 0; rep(i, n) { if (a[i] == total) { wild++; continue; } int x2 = 0; int y2 = -1; rep(j, 32) { ll now = 1LL << x2; if (total - a[i] + now <= 0) { x2++; continue; } if (__builtin_popcountll(total - a[i] + now) == 1) { y2 = 63 - __builtin_clzll(total - a[i] + now); break; } x2++; } if (y2 == -1) { cout << "No\n"; return; } int re = rem[y2]; int ad = add[x2]; if (re) { rem[y2]--; } else { add[y2]++; } if (ad) { add[x2]--; } else { rem[x2]++; } } rep(i, 32) { if (rem[i] != add[i] || rem[i] > wild) { cout << "No\n"; return; } wild -= rem[i]; } cout << "Yes\n"; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); pre(); int t; (TEST && cin >> t) || (t = 1); while (t--) { solve(); } }