#include <bits/stdc++.h>
using namespace std;
bool canPartitionSliding(vector<int>& window) {
int K = window.size();
int total = accumulate(window.begin(), window.end(), 0);
if (total % 2 != 0) return false;
int target = total / 2;
unordered_map<int,int> dp;
dp[0] = 1; // sum 0 is always possible
// initialize first window DP
for (int x : window) {
unordered_map<int,int> new_dp(dp);
for (auto& p : dp) {
new_dp[p.first + x] += p.second;
}
dp = move(new_dp);
}
return dp.count(target);
}
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T;
cin >> T;
while(T--) {
int n;
cin >> n;
vector<int> A(n);
for (int i=0; i<n; i++) cin >> A[i];
vector<bool> valid(n+1, false);
for (int K=2; K<=n; K++) {
if (valid[K]) continue;
bool ok = true;
vector<int> window(A.begin(), A.begin() + K);
if (!canPartitionSliding(window)) ok = false;
for (int i=1; i+K<=n && ok; i++) {
// slide window: remove A[i-1], add A[i+K-1]
window.erase(window.begin());
window.push_back(A[i+K-1]);
if (!canPartitionSliding(window)) {
ok = false;
break;
}
}
if (ok) {
for (int m=K; m<=n; m+=K) valid[m] = true;
}
}
vector<int> ans;
for (int k=2; k<=n; k++) if (valid[k]) ans.push_back(k);
if (ans.empty()) cout << -1 << "\n";
else {
cout<<ans.size()<<' ';
for (int k : ans) cout << k << " ";
cout << "\n";
}
}
return 0;
}
