#include<bits/stdc++.h>
#define int long long
#define endl '\n'
using namespace std;
const int MAXN=5e5+5;
int a[MAXN],n,k;
bool check(int x)
{
    if(x==1) return 1;
    multiset<int> small,big;
    int suma=0,sumb=0;
    auto insert=[&](int temp)
    {
        if(small.size()<=big.size())
        {
            small.insert(temp);
            suma+=temp;
            if(big.size() && *small.rbegin()>*big.begin())
            {
                int x=*small.rbegin(),y=*big.begin();
                small.erase(small.find(x));
                suma-=x;
                big.erase(big.find(y));
                sumb-=y;
                small.insert(y);big.insert(x);
                suma+=y;sumb+=x;
            }
        }
        else
        {
            big.insert(temp);
            sumb+=temp;
            if(small.size() && *small.rbegin()>*big.begin())
            {
                int x=*small.rbegin(),y=*big.begin();
                small.erase(small.find(x));
                suma-=x;
                big.erase(big.find(y));
                sumb-=y;
                small.insert(y);big.insert(x);
                suma+=y;sumb+=x;
            }
        }
    };
    auto del=[&](int temp)
    {
        if(small.size() && temp<=*small.rbegin()) small.erase(small.find(temp)),suma-=temp;
        else big.erase(big.find(temp)),sumb-=temp;
    };


    for(int i=1;i<=n;i++)
    {
        if(i<=x) insert(a[i]);
        else
        {
            del(a[i-x]);
            insert(a[i]);
        }
        if(i>=x)
        {
            int mid;
            if(x%2) mid=*small.rbegin();
            else mid=(*small.rbegin()+*big.begin())/2;
            // if(x==5) cerr<<mid<<' '<<suma<<' '<<sumb<<endl;
            int cha=sumb-(big.size()*mid)+(small.size()*mid)-suma;
            if(cha<=k) return 1;
        }
    }
    return 0;
}
void solve()
{   
    cin>>n>>k;
    vector<int> a(n+1);
    for(int i=1;i<=n;i++) cin>>a[i],a[i]-=i;
    // for(int i=1;i<=n;i++) cerr<<a[i]<<' ';
    // cerr<<endl;
    int l=1,r=n+1;
    while(l<r)
    {
        int mid=l+r>>1;
        if(check(mid)) l=mid+1;
        else r=mid;
    }
    cout<<l-1<<endl;
}
signed main()
{
    cin.tie(0)->sync_with_stdio(0);
    int t=1;
    cin>>t;
    while(t--) solve();
    return 0;
}