#pragma GCC optimize(2, 3)
#include<bits/stdc++.h>
using namespace std;

//#define int long long
using ll = long long;
#define endl '\n'

void solve();
int32_t main()
{
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);

    int tt = 1;
    cin >> tt;

    while (tt--)solve();
    return 0;
}
vector< multiset<int>::iterator > sit(5e5 + 10);
vector<int> a(5e5 + 10);

void solve()
{
    int n;
    ll k;
    cin >> n >> k;

    // vector<int> a(n + 1);
    for (int i = 1; i <= n; i++)cin >> a[i];
    for (int i = 1; i <= n; i++)a[i] -= i;

    int l = 0, r = n + 1;

    auto check = [&](int mid)->bool {
        multiset<int> s;
        int len = mid;
        int x = (len + 1) / 2;
        int L = 0, R = 0;
        for (int i = 1; i <= len; i++)
        {
            s.insert(a[i]);
        }

        auto it = s.begin();
        for (int i = 1; i < x; i++)it++;

        int res = 1e18;
        int now = *it;

        for (int i = 1; i <= len; i++)
        {
            if (a[i] <= now)
            {
                L += a[i];
            }
            else R += a[i];
        }
        int ans = 1e18;
        auto c = [&](int L, int R)
        {
            return abs(L - now * x) + abs(R - now * (len - x));
        };
        res = c(L, R);
        ans = res;
        for (int i = len + 1; i <= n; i++)
        {
            s.insert(a[i]);
            if (a[i] > now)
            {
                // res += a[i] - now;
                L += *it;
                R -= *it;
                it++;
                R += a[i];
                int j = i - len;
                int vj = a[j];

                now = *it;

                if (vj < now)
                {
                    //L -= 
                    L -= vj;
                    s.erase(s.find(vj));
                    //res -= now - vj;
                }
                else if (vj > now)
                {
                    R -= vj;

                    it--;
                    L -= *it;
                    R += *it;
                    s.erase(s.find(vj));
                    // res -= vj - now;
                }
                else if (vj == now)
                {
                    it = s.erase(it);
                    L -= vj;
                }
                res = c(L, R);
                ans = min(res, ans);
                if (ans <= k)return 1;


            }
            else
            {
                // res += now - a[i];
                R += *it;
                L -= *it;
                it--;
                L += a[i];
                int j = i - len;
                int vj = a[j];

                now = *it;


                if (vj < now)
                {
                    L += *it;
                    R -= *it;
                    it++;
                    s.erase(s.find(vj));
                    //res -= now - vj;
                }
                else if (vj > now)
                {

                    s.erase(s.find(vj));

                    // res -= vj - now;
                }
                else if (vj == now)
                {
                    it = s.erase(it);
                    L -= vj;
                }
                ans = min(res, ans);
                if (ans <= k)return 1;
            }
            now = *it;
        }
        return ans <= k;
    };
    auto cc = [&](ll U, ll S, ll now, ll len) -> long long
    {
        if (len & 1)
        {
            return abs(U - (S - U - now));
        }
        else
        {
            return abs(U + now - (S - U - now));
        }
    };
    //vector< multiset<int>::iterator > sit(n + 1);
    // for (int i = 1; i <= n; i++)cout << a[i] << ' '; cout << endl;
#define nums a
    auto ochec = [&](int len) -> int
    {

        //  cout << "len == " << len << endl;

        //multiset<int> s(nums.begin() + 1, nums.begin() + 1 + len);
        multiset<int> s;
        for (int i = 1; i <= len; i++)
        {
            sit[i] = s.insert(nums[i]);
        }
        auto it = s.begin();

        for (int i = 0; i < len / 2; i++)it++;

        int now = *it;

        /*auto c = [&](int L, int R) -> long long
        {
            return abs(L - now * (len / 2 + 1)) + abs(R - now * (len - (len / 2 + 1)));
        };*/
        ll S = 0;
        ll U = 0;

        ll ans = 1e18;

        //int L = 0, R = 0;
        auto tit = s.begin();
        for (int i = 1; i <= len; i++, tit++)
        {
            //if (i <= len / 2 + 1)
            //{
            //    // L += *tit;
            //}
           // sit[i] = tit;
            if (i > len / 2 + 1)
            {
                //R += *tit;
                U += *tit;
            }
            S += *tit;

        }

        now = *it;
        // ans = c(L, R);
        ans = cc(U, S, now, len);
        if (ans <= k)return 1;
        for (int p = len + 1; p <= n; p++)
        {
            // cout << "*it == " << (*it) << '\n';
            sit[p] = s.insert(nums[p]);
            S += nums[p];
            if (nums[p] < (*it))
            {
                // L += nums[p];
                 //R += *it;
                 //L -= *it;
                U += *it;
                it--;
            }
            else U += nums[p];

            if (nums[p - len] <= (*it))
            {
                // U -= *it;
                 //L -= nums[p - len];
                 //R -= *it;
                 //L += *it;
                it++;
                U -= *it;
            }
            else U -= nums[p - len];
            //s.erase(s.lower_bound(nums[p - len]));
            s.erase(sit[p - len]);
            S -= nums[p - len];
            now = *it;
            // ans = min(ans, c(L, R));
            ans = min(ans, cc(U, S, now, len));
            if (ans <= k)return 1;
        }
        return ans <= k;
    };
    while (l < r - 1)
    {
        int mid = l + r >> 1;
        if (ochec(mid))l = mid;
        else r = mid;
    }
    //  cout << "l == ";
    cout << l << endl;
}