#define TLE ios::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
#include "../template/debug.h"
#else 
#define dbg(...) ;
#endif
using ll =long long;
// #define int ll
#define inf 0x3f3f3f3f
#define LINF 0x3f3f3f3f3f3f3f3f
#define rep(i,a,n) for (int i=a;i<=n;i++)
#define per(i,n,a) for (int i=n;i>=a;i--)
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
#define pb push_back
typedef pair<int,int> PII;
// const int mod=1e9+7;
const int mod=998244353;
typedef double db;
mt19937 rnd(time(0));
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
const int N = 5e5+5;
int a[N];
int n;
ll k;
bool check(int mid){
    multiset<int>s1,s2;
    ll sum1=0,sum2=0;
    for(int i=1;i<=n;i++){
        if(i<=mid) {
            s1.insert(a[i]);
            sum1+=a[i];
        }
        else{
            auto it = s1.find(a[i-mid]);
            if(it!=s1.end()) {
                sum1-=*it;
                s1.erase(it);
            }
            else{
                sum2-=a[i-mid];
                s2.erase(s2.find(a[i-mid]));
            }
            if(a[i]>=*s1.begin()) {
                sum1+=a[i];
                s1.insert(a[i]);
            }
            else{
                sum2+=a[i];
                s2.insert(a[i]);
            }
        }
        if(i>=mid){
            while(s1.size()>s2.size()+1) {
                sum2+=*s1.begin();
                sum1-=*s1.begin();
                s2.insert(*s1.begin());
                s1.erase(s1.begin());
            }
            while(s1.size()<s2.size()+1) {
                sum1+=*s2.rbegin();
                sum2-=*s2.rbegin();
                s1.insert(*s2.rbegin());
                s2.erase(--s2.end());
            }
            ll res=sum1 - 1ll*(*s1.begin()) * SZ(s1) + 1ll*(*s1.begin()) * SZ(s2) - sum2; 
            if(res<=k) return 1;
        }
    }
    return 0;
}
int main(){
    TLE;
    int t;
    cin>>t;
    while(t--){
        cin>>n>>k;
        for(int i=1;i<=n;i++){
            cin>>a[i];
            a[i]-=i;
        }
        int l=1,r=n;
        int ans=1;
        while(l<=r){
            int mid = l+r>>1;
            if(check(mid)){
                ans=max(ans,mid);
                l=mid+1;
            }
            else{
                r=mid-1;
            }
        }
        cout<<ans<<'\n';
    }
    return 0;
}