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

#include<ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
typedef tree<double,null_type,less<double>,rb_tree_tag,tree_order_statistics_node_update> rbt_t;

struct tree_t{
	rbt_t rbt;
	int tim;
	tree_t(){tim=0;}
	void init(){
		tim=0;
		rbt.clear();
	}

	void ins(int x){
		++tim;
		rbt.insert(x+tim*1e-6);
	}

	void del(int x){
		rbt.erase(rbt.lower_bound(x));
	}

	int kth(int k){
		return round(*rbt.find_by_order(k-1));
	}
};

template<typename Tp>
Tp read(){
	Tp res=0,sign=1;
	char ch=getchar();
	for(;ch<'0'||ch>'9';ch=getchar())if(ch=='-'){sign=-sign;}
	for(;ch>='0'&&ch<='9';ch=getchar()){res=(res<<3)+(res<<1)+(ch^'0');}
	return res*sign;
}

#define rep(i,l,r) for(int i=l;i<=r;++i)
#define dep(i,r,l) for(int i=r;i>=l;--i)

typedef long long ll;

const int N=5e5+10;

int n;
ll k;

int a[N];

tree_t T;	

bool check(int len){
	ll res=0;
	T.init();
	rep(i,1,len){
		T.ins(a[i]);
	}
	int f=T.kth((len+1)/2);
	rep(i,1,len){
		res+=abs(a[i]-f);
	}
	ll ans=res;
	rep(i,len+1,n){
		T.del(a[i-len]),T.ins(a[i]);
		res=res-abs(a[i-len]-f)+abs(a[i]-f);
		int _f=T.kth((len+1)/2);
		res-=abs(_f-f);
		f=_f;
		ans=min(ans,res);
	}
	return ans<=k;
}

void solve(){
	// n=read<int>(),k=read<ll>();
	scanf("%d%lld",&n,&k);
	// rep(i,1,n)a[i]=read<int>()-i;
	rep(i,1,n)scanf("%d",&a[i]),a[i]-=i;
	int l=1,r=n;
	while(l<=r){
		int mid=l+r>>1;
		if(check(mid))l=mid+1;
		else r=mid-1;
	}
	printf("%d\n",r);
}

int main(){
	// int t=read<int>();
	int t;scanf("%d",&t);
	while(t--)solve();
	return 0;
}