#include <bits/stdc++.h>
using namespace std;
// Function to check if array segment can be partitioned into 2 equal-sum subsequences
bool canPartition(const vector<int>& arr) {
int sum = accumulate(arr.begin(), arr.end(), 0);
if (sum % 2 != 0) return false; // must be even
int target = sum / 2;
bitset<10001> dp; // adjust size if needed
dp[0] = 1;
for (int x : arr) {
dp |= (dp << x);
if (target < (int)dp.size() && dp[target]) return true; // early exit
}
return dp[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; // already marked as multiple of smaller K
bool ok = true;
for (int i=0; i+K<=n; i++) {
vector<int> window(A.begin()+i, A.begin()+i+K);
if (!canPartition(window)) { ok = false; break; }
}
if (ok) {
// mark all multiples of K as valid
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()<<endl;
for (int k : ans) cout << k << " ";
cout << "\n";
}
}
return 0;
}
