# include <bits/stdc++.h>
using namespace std;
# define IOS ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
# define int long long
# define lowbit(x) (x & (-x))
# define fi first
# define se second
# define all(x) x.begin(), x.end()

// # define endl '\n'

inline int Read();

typedef pair<int, int> PII;
const int INF = 0x3f3f3f3f;
const int MOD = 998244353;
const int N = 1e6 + 10;

vector <int> v;

int a[N];
int n, m;
int ok(int x){
    map <int, int> mp1;
    map <int, int> mp2;
    priority_queue<int, vector <int>, less <int>> q;// 大根堆 存小值
    priority_queue<int, vector <int>, greater <int>> p;// 小根堆 存大值
    if(x == 1) return 1;
    int k = (x + 1) / 2;
    int sum1 = 0, sum2 = 0;
    int num1 = 0, num2 = 0;
    for(int i = 1; i <= n; i ++){
        if(num1 < k){
            num1 ++;
            sum1 += a[i];
            mp1[a[i]] ++;
            q.push(a[i]);
        }else{
            p.push(a[i]);
            num2 ++;
            sum2 += a[i];
            mp2[a[i]] ++;
            while(q.size() && mp1[q.top()] == 0) q.pop();
            while(p.size() && mp2[p.top()] == 0) p.pop();
            while(q.top() > p.top()){
                int u, v; 
                u = q.top(); v = p.top();
                q.pop(); p.pop();
                mp1[u] --; sum1 -= u;
                mp2[v] --; sum2 -= v;
                q.push(v);
                p.push(u);
                mp2[u] ++; sum2 += u;
                mp1[v] ++; sum1 += v;
                while(q.size() && mp1[q.top()] == 0) q.pop();
                while(p.size() && mp2[p.top()] == 0) p.pop();
            }
        }
        if(i > x){
            int t = a[i - x];
            if(t <= q.top()){
                sum1 -= t;
                num1 --;
                mp1[t] --;
            }else{
                sum2 -= t;
                num2 --;
                mp2[t] --;
            }
            while(p.size() && mp2[p.top()] == 0) p.pop();
            while(num1 < k){
                int v; 
                v = p.top();
                p.pop();
                num1 ++;
                num2 --;
                mp2[v] --; sum2 -= v;
                q.push(v);
                mp1[v] ++; sum1 += v;
                while(p.size() && mp2[p.top()] == 0) p.pop();
                if(p.size() == 0) break;
            }
        }
        // cout << i <<" " << sum1 <<" " <<num1 <<" * "<< sum2 <<" "<< num2 <<"\n";
        if(i >= x){
            // cout <<num1 * q.top() - sum1 + sum2 - num2 * q.top()<<"****\n"; 
            if(num1 * q.top() - sum1 + sum2 - num2 * q.top() <= m) return 1;
        }
    }
    return 0;
}
void Solve(){
    cin >> n >> m;
    for(int i = 1; i <= n; i ++){
        cin >> a[i];
        a[i] -= i;
    }
    int l = 1, r = n, mid;
    while(l < r){
        mid = l + r + 1 >> 1;
        if(ok(mid)) l = mid;
        else r = mid - 1;
    }
    cout << l <<"\n";
    // ok(3);
}
signed main(){
    // IOS;
    int T = 1;
    cin >> T;
    while (T--) 
        Solve();
    return 0;
}
inline int Read(){
    int x = 0, f = 1; char c = getchar();
    while (c < '0' || c > '9'){ if (c == '-') f = -1; c = getchar();}
    while (c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}