思路:
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pb push_back
#define fi first
#define se second
#define lson p << 1
#define rson p << 1 | 1
const int maxn = 1e6 + 5, inf = 1e18, maxm = 4e4 + 5, mod = 1e9 + 7, N = 1e6;
// int a[505][5005];
// bool vis[505][505];
// char s[505][505];
int a[maxn];
bool vis[maxn];
string s;
int n, m;
struct Node{
// int val, id;
// bool operator<(const Node &u)const{
// return val < u.val;
// }
int x, y;
}c[maxn];
void calc(int d, int &x, int &y){
x = -1, y = -1;
for(int i = 0; i <= 31; i++){
for(int j = 0; j <= i; j++){
if(d == (1LL << i) - (1LL << j)){
x = i;
y = j;
return;
}
}
}
}
void solve(){
int res = 0;
int q, k;
cin >> n;
int from[35] = {0}, to[35] = {0};
int x, y;
int sum = 0;
for(int i = 1; i <= n; i++){
cin >> a[i];
sum += a[i];
}
if(sum % n != 0){
cout << "No\n";
return;
}
int ave = sum / n;
for(int i = 1; i <= n; i++){
int d = abs(ave - a[i]);
calc(d, x, y);
if(x == -1){
cout << "No\n";
return;
}
if(a[i] < ave){
to[x]++;
from[y]++;
}
else{
to[y]++;
from[x]++;
}
}
for(int i = 0; i <= 31; i++){
if(from[i] != to[i]){
cout << "No\n";
return;
}
}
cout << "Yes\n";
}
signed main(){
ios::sync_with_stdio(0);
cin.tie(0);
int T = 1;
cin >> T;
while (T--)
{
solve();
}
return 0;
}