#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;
const int inf = 1e18 + 10;

int n, a[N], m;


void sol() {
    cin >> n >> m;
    F(i, 1, n) cin >> a[i];
    F(i, 1, n) a[i] -= i;

    multiset<int> s1, s2;
    int sum1 = 0, sum2 = 0;
    int tot = 0;

    auto adjust = [&](auto adjust) -> void {
        int sz = tot + 1 >> 1;
        while(s1.size() > sz) {
            int now = *s1.rbegin();
            s1.erase(s1.find(now)), s2.insert(now);
            sum1 -= now, sum2 += now;
        } 
        while(s1.size() < sz) {
            int now = *s2.begin();
            s2.erase(s2.find(now)), s1.insert(now);
            sum1 += now, sum2 -= now;
        }
    };
    auto add = [&](auto add, int x) -> void {
        int tmp = s1.size() ? *s1.rbegin() : -inf;
        if(x < tmp) s1.insert(x), sum1 += x;
        else s2.insert(x), sum2 += x; 
        tot ++;
        adjust(adjust);
    };
    auto del = [&](auto del, int x) -> void {
        int tmp = s1.size() ? *s1.rbegin() : -inf;
        if(x <= tmp) s1.erase(s1.find(x)), sum1 -= x;
        else s2.erase(s2.find(x)), sum2 -= x; 
        tot --;
        adjust(adjust);
    };
    auto get_ans = [&](auto get_ans) -> int {
        if(! tot) return 0;
        int tmp = *s1.rbegin(), n1 = s1.size(), n2 = s2.size();
        return tmp * n1 - sum1 + sum2 - tmp * n2;
    };

    int ans = 0, res = 1;
    for(int l = 1, r = 0; l <= n; l ++) {
        if(l != 1) del(del, a[l - 1]);
        ans = get_ans(get_ans);
        if(ans <= m) res = max(res, tot);
        while((r < l || ans <= m) && r < n) {
            if(r >= l && ans > m) break;
            add(add, a[++ r]);
            ans = get_ans(get_ans);
            if(ans <= m) res = max(res, tot);
        }
    }
    cout << res << "\n";
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int t; cin >> t;
    F(i, 1, t) sol();
    return 0;
}
/*
5
7 5
7 2 5 5 4 11 7
6 0
100 3 4 5 99 100
5 6
1 1 1 1 1
5 50
100 200 300 400 500
1 100
3

*/