#include<bits/stdc++.h>
#define F(i, a, b) for(int i = a; i <= b; i ++)
#define Fd(i, a, b) for(int i = a; i >= b; i --)
#define int long long
#define pii pair<int, int>
#define fi first
#define se second
using namespace std;

const int N = 5e5 + 10;

int n, a[N], m;

bool check(int x) {
    multiset<int> s1, s2;
    int sz1 = (x + 1) / 2, sz2 = x - sz1;
    // cout << x << " " << sz1 << " " << sz2 << endl;
    int sum1 = 0, sum2 = 0;

    F(i, 1, sz1) s1.insert(a[i]), sum1 += a[i];
    F(i, sz1 + 1, x) {
        int nowmid = *s1.rbegin();
        if(nowmid > a[i]) {
            s1.erase(s1.find(nowmid));
            s2.insert(nowmid);
            s1.insert(a[i]);
            sum2 += nowmid;
            sum1 += a[i] - nowmid;
        } else s2.insert(a[i]), sum2 += a[i];
    }
    int mm = *s1.rbegin();
    if((mm * sz1) - sum1 + sum2 - (mm * sz2) <= m) return true;

    // cout << sum1 << " " << sum2 << endl;

    F(i, 2, n - x + 1) {
        int j = i + x - 1; 
        mm = *s1.rbegin();
        if(a[i - 1] <= mm) s1.erase(s1.find(a[i - 1])), sum1 -= a[i - 1];
        else s2.erase(s2.find(a[i - 1])), sum2 -= a[i - 1];
        mm = s1.size() ? *s1.rbegin() : 0;
        if(a[j] <= mm) s1.insert(a[j]), sum1 += a[j];
        else s2.insert(a[j]), sum2 += a[j];
        if(s1.size() < sz1) {
            int now = *s2.begin();
            s2.erase(s2.find(now)), s1.insert(now);
            sum1 += now, sum2 -= now;
        } else if(s1.size() > sz1) {
            int now = *s1.rbegin();
            s1.erase(s1.find(now)), s2.insert(now);
            sum1 -= now, sum2 += now;
        }

        mm = *s1.rbegin();
        if((mm * sz1) - sum1 + sum2 - (mm * sz2) <= m) return true;
    }

    return false;
}

void sol() {
    cin >> n >> m;
    F(i, 1, n) cin >> a[i];
    F(i, 1, n) a[i] -= i;
    int l = 1, r = n;
    while(l < r) {
        int mid = l + r + 1 >> 1;
        if(check(mid)) l = mid;
        else r = mid - 1;
    }
    cout << l << "\n";
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int t; cin >> t;
    F(i, 1, t) sol();
    return 0;
}
/*
1
5 50
100 200 300 400 500

*/