#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
long long binpow(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = (res * x);
    y = y >> 1;
    x = (x * x);
  }
  return res;
}
long long binpowmod(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long mod_inverse(long long n, long long p) {
  return binpowmod(n, p - 2, p);
}
long long gcd(long long x, long long y) {
  if (y == 0) return x;
  return gcd(y, x % y);
}
bool comp_pairs_by_s(pair<long long, long long> &x,
                     pair<long long, long long> &y) {
  return x.second < y.second;
}
bool isPowerOfTwo(long long x) { return x && (!(x & (x - 1))); }
class cmp {
 public:
  bool operator()(pair<int, int> A, pair<int, int> B) {
    if (abs(A.first - A.second) == abs(B.first - B.second))
      return A.first > B.first;
    return abs(A.first - A.second) < abs(B.first - B.second);
  }
};
void swap(long long &x, long long &y) {
  int temp = x;
  x = y;
  y = temp;
}
unsigned int onesComplement(unsigned int n) {
  int number_of_bits = floor(log2(n)) + 1;
  return ((1 << number_of_bits) - 1) ^ n;
}
bool comp(pair<long long, long long> x, pair<long long, long long> y) {
  return x.second < y.second;
}
bool comp1(pair<long long, long long> x, pair<long long, long long> y) {
  return x.second < y.second;
}
void selfmin(int &x, int y) { x = min(x, y); }
void solve() {
  int n;
  cin >> n;
  vector<long long> a(n);
  for (auto &it : a) cin >> it;
  if (a[0] + a[1] > a[n - 1])
    cout << -1;
  else {
    cout << 1 << ' ' << 2 << ' ' << n;
  }
  cout << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) solve();
}

### Prompt

Please formulate a CPP solution to the following problem:

You are given an array a_1, a_2, ... , a_n, which is sorted in non-decreasing order (a_i ≤ a_{i + 1}). 

Find three indices i, j, k such that 1 ≤ i < j < k ≤ n and it is impossible to construct a non-degenerate triangle (a triangle with nonzero area) having sides equal to a_i, a_j and a_k (for example it is possible to construct a non-degenerate triangle with sides 3, 4 and 5 but impossible with sides 3, 4 and 7). If it is impossible to find such triple, report it.

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

The first line of each test case contains one integer n (3 ≤ n ≤ 5 ⋅ 10^4) — the length of the array a.

The second line of each test case contains n integers a_1, a_2, ... , a_n (1 ≤ a_i ≤ 10^9; a_{i - 1} ≤ a_i) — the array a.

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case print the answer to it in one line.

If there is a triple of indices i, j, k (i < j < k) such that it is impossible to construct a non-degenerate triangle having sides equal to a_i, a_j and a_k, print that three indices in ascending order. If there are multiple answers, print any of them.

Otherwise, print -1.

Example

Input


3
7
4 6 11 11 15 18 20
4
10 10 10 11
3
1 1 1000000000


Output


2 3 6
-1
1 2 3

Note

In the first test case it is impossible with sides 6, 11 and 18. Note, that this is not the only correct answer.

In the second test case you always can construct a non-degenerate triangle.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
long long binpow(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = (res * x);
    y = y >> 1;
    x = (x * x);
  }
  return res;
}
long long binpowmod(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long mod_inverse(long long n, long long p) {
  return binpowmod(n, p - 2, p);
}
long long gcd(long long x, long long y) {
  if (y == 0) return x;
  return gcd(y, x % y);
}
bool comp_pairs_by_s(pair<long long, long long> &x,
                     pair<long long, long long> &y) {
  return x.second < y.second;
}
bool isPowerOfTwo(long long x) { return x && (!(x & (x - 1))); }
class cmp {
 public:
  bool operator()(pair<int, int> A, pair<int, int> B) {
    if (abs(A.first - A.second) == abs(B.first - B.second))
      return A.first > B.first;
    return abs(A.first - A.second) < abs(B.first - B.second);
  }
};
void swap(long long &x, long long &y) {
  int temp = x;
  x = y;
  y = temp;
}
unsigned int onesComplement(unsigned int n) {
  int number_of_bits = floor(log2(n)) + 1;
  return ((1 << number_of_bits) - 1) ^ n;
}
bool comp(pair<long long, long long> x, pair<long long, long long> y) {
  return x.second < y.second;
}
bool comp1(pair<long long, long long> x, pair<long long, long long> y) {
  return x.second < y.second;
}
void selfmin(int &x, int y) { x = min(x, y); }
void solve() {
  int n;
  cin >> n;
  vector<long long> a(n);
  for (auto &it : a) cin >> it;
  if (a[0] + a[1] > a[n - 1])
    cout << -1;
  else {
    cout << 1 << ' ' << 2 << ' ' << n;
  }
  cout << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) solve();
}

```