Problem: You have a knapsack with the capacity of W. There are also n items, the i-th one has weight w_i. 

You want to put some of these items into the knapsack in such a way that their total weight C is at least half of its size, but (obviously) does not exceed it. Formally, C should satisfy: ⌈ W/2⌉ ≤ C ≤ W. 

Output the list of items you will put into the knapsack or determine that fulfilling the conditions is impossible. 

If there are several possible lists of items satisfying the conditions, you can output any. Note that you don't have to maximize the sum of weights of items in the knapsack.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows.

The first line of each test case contains integers n and W (1 ≤ n ≤ 200 000, 1≤ W ≤ 10^{18}). 

The second line of each test case contains n integers w_1, w_2, ..., w_n (1 ≤ w_i ≤ 10^9) — weights of the items.

The sum of n over all test cases does not exceed 200 000.

Output

For each test case, if there is no solution, print a single integer -1. 

If there exists a solution consisting of m items, print m in the first line of the output and m integers j_1, j_2, ..., j_m (1 ≤ j_i ≤ n, all j_i are distinct) in the second line of the output — indices of the items you would like to pack into the knapsack.

If there are several possible lists of items satisfying the conditions, you can output any. Note that you don't have to maximize the sum of weights items in the knapsack.

Example

Input


3
1 3
3
6 2
19 8 19 69 9 4
7 12
1 1 1 17 1 1 1


Output


1
1
-1
6
1 2 3 5 6 7

Note

In the first test case, you can take the item of weight 3 and fill the knapsack just right.

In the second test case, all the items are larger than the knapsack's capacity. Therefore, the answer is -1.

In the third test case, you fill the knapsack exactly in half.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization("unroll-loops")
using namespace std;
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
void io() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin.tie(0);
}
long long gcd(long long a, long long b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
long long div(long long a, long long b, long long m) {
  if (a % m == 0)
    return ((b / m) - (a / m) + 1);
  else
    return ((b / m) - (a / m));
}
struct dsu {
  vector<long long> par;
  dsu(long long n) {
    par.resize(n + 1);
    iota(par.begin(), par.end(), 0);
  }
  long long get(long long x) {
    if (par[x] == x) return par[x];
    par[x] = get(par[x]);
    return par[x];
  }
  void unite(long long x, long long y) {
    x = get(x);
    y = get(y);
    par[x] = par[y];
  }
};
void SieveOfEratosthenes(vector<long long> &a) {
  bool prime[100005];
  memset(prime, true, sizeof(prime));
  for (long long p = 2; p * p < 100005; p++) {
    if (prime[p] == true) {
      for (long long i = p * p; i < 100005; i += p) prime[i] = false;
    }
  }
  for (long long p = 2; p < 100005; p++) {
    if (prime[p]) a[p] = p;
  }
}
bool cmp(pair<long long, pair<long long, long long>> a,
         pair<long long, pair<long long, long long>> b) {
  if (a.second.second == b.second.second) {
    if (a.second.first == b.second.first) {
      return a.first < b.first;
    } else
      return a.second.first < b.second.first;
  } else
    return a.second.second < b.second.second;
}
const long long N = 1e5;
vector<long long> gr[N];
long long vis[N + 1];
long long depth[N + 1];
void bfs_tree(long long source) {
  queue<long long> Q;
  Q.push(source);
  vis[source] = 1;
  while (!Q.empty()) {
    long long cur = Q.front();
    Q.pop();
    cout << cur << " ";
    for (auto x : gr[cur]) {
      if (!vis[x]) {
        vis[x] = 1;
        Q.push(x);
      }
    }
  }
}
void dfsGraph(long long curr) {
  cout << curr << "->";
  vis[curr] = 1;
  for (auto x : gr[curr]) {
    if (!vis[x]) dfsGraph(x);
  }
  return;
}
void dfsGraphWithoutVistedArray(long long curr, long long par) {
  cout << curr << "->";
  for (auto x : gr[curr]) {
    if (x != par) dfsGraphWithoutVistedArray(x, curr);
  }
  return;
}
long long checkPrime(long long n) {
  long long flag = 0;
  for (long long i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      flag = 1;
      break;
    }
  }
  if (flag == 1)
    return 0;
  else
    return 1;
}
long long mo = 1e9 + 7;
long long binpow(long long a, long long b, long long m) {
  a %= m;
  long long res = 1;
  while (b > 0) {
    if (b & 1) res = res * a % m;
    a = a * a % m;
    b >>= 1;
  }
  return res;
}
long long mul_mod(long long a, long long b) {
  return ((a % mo) * (b % mo)) % mo;
}
long long add_mod(long long a, long long b) {
  return ((a % mo) + (b % mo)) % mo;
}
long long diff_mod(long long a, long long b) {
  return ((a % mo) - (b % mo)) % mo;
}
long long mod_inv(long long a, long long m) {
  long long val = binpow(a, m - 2, m);
  return val;
}
const long long NN = 500005;
long long fact[NN];
long long inver[NN];
void precompute() {
  fact[0] = 1;
  inver[0] = 1;
  long long pro = 1;
  for (long long i = 1; i < NN; i++) {
    pro = mul_mod(i, pro);
    fact[i] = pro;
    inver[i] = mod_inv(fact[i], mo);
  }
}
long long nck(long long n, long long k) {
  if (k > n or k < 0) return 0;
  long long ans = fact[n];
  ans = mul_mod(ans, inver[n - k]);
  ans = mul_mod(ans, inver[k]);
  return ans;
}
long long solve() {
  long long n, k, x, y;
  cin >> n >> k;
  vector<pair<long long, long long>> v;
  for (long long i = 0; i < n; i++) {
    cin >> x >> y;
    v.push_back({x, y});
  }
  precompute();
  sort(v.begin(), v.end());
  multiset<long long> ms;
  long long ans = 0;
  for (long long i = 0; i < n; i++) {
    while (!ms.empty() and (*ms.begin() < v[i].first)) ms.erase(ms.begin());
    long long cal_comb = nck(ms.size(), k - 1);
    ans = add_mod(cal_comb, ans);
    ms.insert(v[i].second);
  }
  cout << ans << "\n";
}
void suffix_sum(long long suffix[], long long a[], long long m) {
  suffix[m - 1] = a[m - 1];
  for (long long i = m - 2; i >= 0; i--) suffix[i] = a[i] + suffix[i + 1];
}
void pre_sum(long long pre[], long long a[], long long m) {
  pre[0] = a[0];
  for (long long i = 1; i, m; i++) pre[i] = a[i] + pre[i - 1];
}
int32_t main() {
  io();
  vector<long long> a(100005, 0);
  SieveOfEratosthenes(a);
  cout << fixed;
  cout.precision(10);
  long long t;
  cin >> t;
  while (t--) {
    long long n, m, k, x, y, z, w, l, r, q, p, num, x1, y1, x2, y2;
    string s;
    long long sum = 0;
    long long small = INT_MAX;
    long long big = INT_MIN;
    map<long long, long long> make_pair;
    long long ans = INT_MAX;
    long long flag = 0;
    cin >> n >> w;
    vector<pair<long long, long long>> v;
    for (long long i = 0; i < n; i++) {
      cin >> x;
      sum += x;
      small = min(small, x);
      v.push_back({x, i + 1});
    }
    sort(v.rbegin(), v.rend());
    long long cal = (w + 1) / 2;
    if (small > w or sum < cal)
      cout << -1 << "\n";
    else {
      vector<long long> vv;
      sum = 0;
      for (long long i = 0; i < n; i++) {
        if (sum + v[i].first <= w) {
          vv.push_back(v[i].second);
          sum += v[i].first;
        }
      }
      if (sum < cal)
        cout << -1 << "\n";
      else {
        cout << vv.size() << "\n";
        for (long long i = 0; i < vv.size(); i++) cout << vv[i] << " ";
        cout << "\n";
      }
    }
  }
  return 0;
}