#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int t;
    cin >> t;
    while(t--) {
        int n;
        long long k;
        cin >> n >> k;
        vector<int>a(n);
        for(int i = 0; i < n; i++) {
            cin >> a[i];
            a[i] -= i;
        }
        int l = 1,r = n+1;
        while(l+1 < r) {
            int mid = (l+r)/2;
            multiset<int>st1,st2;
            long long sum1 = 0,sum2 = 0;
            for(int i = 0; i < mid; i++) {
                st1.insert(a[i]);
                sum1 += a[i];
                if(st1.size() > st2.size()+1) {
                    int b = *st1.rbegin();
                    sum1 -= b;
                    sum2 += b;
                    st2.insert(b);
                    st1.erase(st1.find(b));
                }
            }
            bool flag = false;
            int b = *st1.rbegin();
            if(sum2-1ll*st2.size()*b+1ll*st1.size()*b-sum1 <= k) {
                flag = true;
            }
            for(int i = mid; i < n; i++) {
                if(*st1.rbegin() < a[i]) {
                    st2.insert(a[i]);
                    sum2 += a[i];
                }
                else {
                    st1.insert(a[i]);
                    sum1 += a[i];
                }
                if(st1.count(a[i-mid])) {
                    st1.erase(st1.find(a[i-mid]));
                    sum1 -= a[i-mid];
                }
                else {
                    st2.erase(st2.find(a[i-mid]));
                    sum2 -= a[i-mid];
                }
                while(st1.size() > st2.size()+1) {
                    int b = *st1.rbegin();
                    sum1 -= b;
                    sum2 += b;
                    st2.insert(b);
                    st1.erase(st1.find(b));
                }
                while(st2.size() > st1.size()) {
                    int b = *st2.begin();
                    sum2 -= b;
                    sum1 += b;
                    st1.insert(b);
                    st2.erase(st2.find(b));
                }
                int b = *st1.rbegin();
                if(sum2-1ll*st2.size()*b+1ll*st1.size()*b-sum1 <= k) {
                    flag = true;
                }
            }
            if(flag) {
                l = mid;
            }
            else {
                r = mid;
            }
        }
        cout << l << "\n";
    }
}