#include <bits/stdc++.h>
#define endl '\n'
using namespace std;
using i64 = long long;

struct Info
{
    i64 val = 0;
    int cnt = 0;
};

struct BIT
{
    vector<Info> tree;
    int n;
    BIT(int n) : tree(n + 1), n(n) {}
    inline int lowbit(int n)
    {
        return n & -n;
    }
    void update(int idx, i64 val)
    {
        while (idx <= n)
            tree[idx].val += val, tree[idx].cnt += 1, idx += lowbit(idx);
    }
    void erase(int idx, i64 val)
    {
        while (idx <= n)
            tree[idx].val -= val, tree[idx].cnt -= 1, idx += lowbit(idx);
    }
    pair<i64, i64> querySmall(int idx)
    {
        i64 ans = 0, cnt = 0;
        while (idx)
            ans += (tree[idx].val), cnt += tree[idx].cnt, idx -= lowbit(idx);
        return make_pair(ans, cnt);
    }
    pair<i64, i64> queryBig(int idx)
    {
        auto it = querySmall(idx);
        int id = n;
        i64 res1 = 0, res2 = 0;
        while (id)
            res1 += tree[id].val, res2 += tree[id].cnt, id -= lowbit(id);
        res1 -= it.first, res2 -= it.second;
        return make_pair(res1, res2);
    }
};

// const int N =

void solve()
{
    int n;
    i64 k;
    int timer = 0;
    cin >> n >> k;
    vector<int> a(n + 1);
    vector<int> idx(n + 1);
    vector<int> sorted(n + 1);
    for (int i = 1; i <= n; i++)
    {
        cin >> a[i], a[i] -= i;
        sorted[i] = a[i];
    }
    sort(sorted.begin() + 1, sorted.end());
    sorted.erase(unique(sorted.begin(), sorted.end()), sorted.end());
    // for (int i = 1; i <= n; i++)
    //     cout << a[i] << " \n"[i == n];
    for (int i = 1; i <= n; i++)
        idx[i] = lower_bound(sorted.begin() + 1, sorted.end(), a[i]) - sorted.begin();
    BIT tr(sorted.size() + 1);
    int L = 1, R = n, ans = -1;
    auto check = [&](int mid) -> bool
    {
        // cout << mid << endl;
        for (int i = 1; i <= tr.n; i++)
            tr.tree[i].cnt = tr.tree[i].val = 0;
        multiset<pair<int, int>> s1, s2;
        pair<int, int> middle;
        for (int i = 1; i <= mid; i++)
        {
            s1.insert(make_pair(a[i], i));
            tr.update(idx[i], a[i]);
            while (s1.size() > (mid + 1) / 2)
            {
                auto it = s1.rbegin();
                s2.insert(*it);
                s1.erase(s1.find(*it));
            }
        }
        middle = *s1.rbegin();
        // cout << middle.first << " " << idx[middle.second] << " ";
        auto it1 = tr.queryBig(idx[middle.second]), it2 = tr.querySmall(idx[middle.second]);
        i64 ans = middle.first * it2.second - it2.first + (it1.first - it1.second * middle.first);
        if (ans <= k)
            return true;
        // cout << ans << endl;
        for (int i = mid + 1, j = 1; i <= n; i++, j++)
        {
            tr.erase(idx[j], a[j]);
            if (s1.count(make_pair(a[j], j)))
                s1.erase(s1.find(make_pair(a[j], j)));
            else if (s2.count(make_pair(a[j], j)))
                s2.erase(s2.find(make_pair(a[j], j)));
            while (s1.size() < (mid + 1) / 2 && s2.size())
            {
                auto it = s2.begin();
                s1.insert(*it);
                s2.erase(it);
            }
            tr.update(idx[i], a[i]);
            s1.insert(make_pair(a[i], i));
            while (s1.size() > (mid + 1) / 2)
            {
                auto it = s1.rbegin();
                s2.insert(*it);
                s1.erase(s1.find(*it));
            }
            middle = *s1.rbegin();
            // cout << middle.first << " " << idx[middle.second] << " ";
            it1 = tr.queryBig(idx[middle.second]), it2 = tr.querySmall(idx[middle.second]);
            ans = middle.first * it2.second - it2.first + (it1.first - it1.second * middle.first);
            // cout << ans << endl;
            if (ans <= k)
            {
                // cout << "-------------------------\n";
                return true;
            }
        }
        // cout << "--------------------------\n";
        return false;
    };
    // cout << check(1) << endl;
    while (L <= R)
    {
        int mid = L + R >> 1;
        if (check(mid))
            ans = mid, L = mid + 1;
        else
            R = mid - 1;
    }
    cout << ans << endl;
}

int main()
{
    ios::sync_with_stdio(false), cin.tie(0);
    int T = 1;
    cin >> T;
    while (T--)
        solve();
    // system("pause");
    return 0;
}