#include <bits/stdc++.h>
using namespace std;

#define int long long

const int N = 5e5+5;

int n,k;
int a[N];

int check(int L)
{
	
	vector<int>tmp;
	for(int i=1;i<=L;i++){
		tmp.push_back(a[i]);
	}
	sort(tmp.begin(),tmp.end());
	multiset<int>ar1,ar2;
	for(int i=0;i<L;i++){
		if(i+1<=(L+1)/2) ar1.insert(tmp[i]);
		else ar2.insert(tmp[i]);
	}
	int val = 0;
	for(int i=1;i<=L;i++){
		val += abs((*ar1.rbegin())-a[i]);
	}
	// cout<<ar1.size()<<' '<<ar2.size()<<'\n';
	int s1 = 0,s2 = 0;
	for(int i:ar1) s1 += i;
	for(int i:ar2) s2 += i;
	// cout<<(*ar1.rbegin())<<' '<<s1<<' '<<s2<<' '<<val<<'\n'; 
	for(int i=L+1;i<=n;i++){
		int del = a[i-L];
		if(ar1.lower_bound(del)!=ar1.end()){
			auto it = ar1.lower_bound(del);
			ar1.erase(it);
			s1 -= a[i-L];
			if(*ar2.begin()>=a[i]){
				ar1.insert(a[i]);
				s1 += a[i];
			}else{
				int v = *ar2.begin();
				it = ar2.lower_bound(v);
				ar2.erase(it);
				ar2.insert(a[i]);
				ar1.insert(v);
				s1 += v;
				s2 += a[i]-v;
			}
		}else{
			auto it = ar2.lower_bound(del);
			ar2.erase(it);
			s2 -= a[i-L];
			if(*ar1.rbegin()<=a[i]){
				ar2.insert(a[i]);
				s2 += a[i];
			}else{
				int v = *ar1.rbegin();
				it = ar1.lower_bound(v);
				ar1.erase(it);
				ar1.insert(a[i]);
				ar2.insert(v);
				s2 += v;
				s1 += a[i]-v;
			}
		}
		int t = *ar1.rbegin();
		// cout<<t<<":";
		int cur = (L+1)/2*t-s1 + s2 - (L/2)*t;
		val = min(val,cur);
		// cout<<s1<<' '<<s2<<' '<<val<<'\n';
	}	
	// cout<<'\n';
	// cout<<L<<':'<<val<<'\n';
	// cout<<"---\n";
	return val<=k;
}

void solve()
{
	cin>>n>>k;
	for(int i=1;i<=n;i++){
		cin>>a[i];
		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';
	// cout<<"ans:"<<l<<'\n';
}

signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0),cout.tie(0);
	
	int T;
	cin>>T;
	while(T--){
		solve();
	}
}

// 7 2 5 5 4 11 7
// 6 0 2 1 -1 5 0

// 6 0 2 1 -1 5
// -1 0 1 2 5 6

// 0 2 1 -1 5 0
// -1 0 0 1 2 5