#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define mp make_pair
#define si(x) int(x.size())
const int mod=998244353,MAX=300005;
const ll INF=1LL<<60;

//wavelet matrix topK sum 付き

//Wavelet matrix + range topK sum (small)

// https://kopricky.github.io/code/DataStructure_Advanced/wavelet_matrix.html

struct BitRank {
    // block: bit 列を管理, count: block ごとに立っている 1 の数を管理
    vector<unsigned long long> block;
    vector<unsigned int> count;
    BitRank(){}
    void resize(const unsigned int num){
        block.resize(((num + 1) >> 6) + 1, 0);
        count.resize(block.size(), 0);
    }
    // i ビット目を val(0,1) にセット
    void set(const unsigned int i, const unsigned long long val){
        block[i >> 6] |= (val << (i & 63));
    }
    void build(){
        for(unsigned int i = 1; i < block.size(); i++){
            count[i] = count[i - 1] + __builtin_popcountll(block[i - 1]);
        }
    }
    // [0, i) ビットの 1 の数
    unsigned int rank1(const unsigned int i) const {
        return count[i >> 6] +
        __builtin_popcountll(block[i >> 6] & ((1ULL << (i & 63)) - 1ULL));
    }
    // [i, j) ビットの 1 の数
    unsigned int rank1(const unsigned int i, const unsigned int j) const {
        return rank1(j) - rank1(i);
    }
    // [0, i) ビットの 0 の数
    unsigned int rank0(const unsigned int i) const {
        return i - rank1(i);
    }
    // [i, j) ビットの 0 の数
    unsigned int rank0(const unsigned int i, const unsigned int j) const {
        return rank0(j) - rank0(i);
    }
};

class WaveletMatrix
{
private:
    unsigned int height;
    vector<BitRank> B;
    vector<int> pos;
    vector<vector<ll>> rui;
public:
    WaveletMatrix(){}
    WaveletMatrix(vector<int> vec) :
    WaveletMatrix(vec, *max_element(vec.begin(), vec.end()) + 1){}
    // sigma:文字の種類数
    WaveletMatrix(vector<int> vec, const unsigned int sigma){
        init(vec, sigma);
    }
    void init(vector<int>& vec, const unsigned int sigma){
        height = (sigma == 1) ? 1 : (64 - __builtin_clzll(sigma - 1));
        B.resize(height), pos.resize(height);
        vector<int> A = vec;
        rui.resize(height+1);
        for(unsigned int i = 0; i < height; ++i){
            B[i].resize(vec.size());
            for(unsigned int j = 0; j < vec.size(); ++j) {
                B[i].set(j, get(vec[j], height - i - 1));
            }
            B[i].build();
            auto it = stable_partition(vec.begin(), vec.end(), [&](int c){
                return !get(c, height - i - 1);
            });
            pos[i] = it - vec.begin();
        }
        
        for(unsigned int i = 0; i <= height; ++i){
            rui[i].resize(si(A) + 1);
            for(int j = 1;j <= si(A); j++){
                rui[i][j] = rui[i][j-1] + A[j-1];
            }
            if(i==height) break;
            stable_partition(all(A),[&](int c){
                return !get(c,height-i-1);
            });
        }
    }
    // val の i ビット目の値を返す(0,1)
    int get(const int val, const int i){
        return val >> i & 1;
    }
    // [l, r) の間に現れる値 val の数
    int rank(const int val, const int l, const int r){
        return rank(val, r) - rank(val, l);
    }
    // [0, i) の間に現れる値 val の数
    int rank(int val, int i){
        int p = 0;
        for(unsigned int j = 0; j < height; ++j){
            if(get(val, height - j - 1)){
                p = pos[j] + B[j].rank1(p);
                i = pos[j] + B[j].rank1(i);
            }else{
                p = B[j].rank0(p);
                i = B[j].rank0(i);
            }
        }
        return i - p;
    }
    // [l, r) の k(0,1,2...) 番目に小さい値を返す
    int quantile(int k, int l, int r){
        int res = 0;
        for(unsigned int i = 0; i < height; ++i){
            const int j = B[i].rank0(l, r);
            if(j > k){
                l = B[i].rank0(l);
                r = B[i].rank0(r);
            }else{
                l = pos[i] + B[i].rank1(l);
                r = pos[i] + B[i].rank1(r);
                k -= j;
                res |= (1 << (height - i - 1));
            }
        }
        return res;
    }
    ll topKsum(int k,int l,int r){
        if(l==r) return 0LL;
        ll res = 0;
        int atai = 0;
        for(unsigned int i = 0; i < height; ++i){
            const int j = B[i].rank0(l, r);
            if(j > k){
                l = B[i].rank0(l);
                r = B[i].rank0(r);
            }else{
                int l2 = B[i].rank0(l);
                int r2 = B[i].rank0(r);
                res += rui[i+1][r2] - rui[i+1][l2];
                
                l = pos[i] + B[i].rank1(l);
                r = pos[i] + B[i].rank1(r);
                k -= j;
                
                atai |= (1 << (height - i - 1));
            }
        }
        res += (ll) atai * k;
        return res;
    }
    int rangefreq(const int i, const int j, const int a, const int b,
                  const int l, const int r, const int x){
        if(i == j || r <= a || b <= l) return 0;
        const int mid = (l + r) >> 1;
        if(a <= l && r <= b){
            return j - i;
        }else{
            const int left = rangefreq(B[x].rank0(i), B[x].rank0(j), a, b, l, mid, x + 1);
            const int right = rangefreq(pos[x] + B[x].rank1(i), pos[x] + B[x].rank1(j),
                                        a, b, mid, r, x + 1);
            return left + right;
        }
    }
    // [l,r) で値が [a,b) 内に含まれる数を返す
    int rangefreq(const int l, const int r, const int a, const int b){
        return rangefreq(l, r, a, b, 0, 1 << height, 0);
    }
    int rangemin(const int i, const int j, const int a, const int b,
                 const int l, const int r, const int x, const int val){
        if(i == j || r <= a || b <= l) return -1;
        if(r - l == 1) return val;
        const int mid = (l + r) >> 1;
        const int res = rangemin(B[x].rank0(i),B[x].rank0(j),a,b,l,mid,x+1,val);
        if(res < 0) return rangemin(pos[x] + B[x].rank1(i), pos[x] + B[x].rank1(j),
                                    a, b, mid, r, x + 1, val + (1 << (height - x - 1)));
        else return res;
    }
    // [l,r) で値が [a,b) 内に最小の数を返す(数が存在しない場合は -1 を返す)
    int rangemin(int l, int r, int a, int b){
        return rangemin(l, r, a, b, 0, 1 << height, 0, 0);
    }
};

template<typename T> class OrthogonalRangeCount
{
private:
    using ptt = pair<T, T>;
    const int sz;
    vector<T> X, Y;
    WaveletMatrix wm;
    
public:
    OrthogonalRangeCount(vector<ptt> candidate)
    : sz((int)candidate.size()), X(sz), Y(sz){
        sort(candidate.begin(), candidate.end());
        vector<int> vec(sz);
        for(int i = 0; i < sz; ++i){
            X[i] = candidate[i].first, Y[i] = candidate[i].second;
        }
        sort(Y.begin(), Y.end());
        Y.erase(unique(Y.begin(), Y.end()), Y.end());
        for(int i = 0; i < sz; ++i){
            vec[i] = lower_bound(Y.begin(), Y.end(), candidate[i].second) - Y.begin();
        }
        wm.init(vec, Y.size());
    }
    // [lx,rx) × [ly, ry) の長方形領域に含まれる点の数を答える
    int query(const T lx, const T ly, const T rx, const T ry){
        const int lxid = lower_bound(X.begin(), X.end(), lx) - X.begin();
        const int rxid = lower_bound(X.begin(), X.end(), rx) - X.begin();
        const int lyid = lower_bound(Y.begin(), Y.end(), ly) - Y.begin();
        const int ryid = lower_bound(Y.begin(), Y.end(), ry) - Y.begin();
        if(lxid >= rxid || lyid >= ryid) return 0;
        return wm.rangefreq(lxid, rxid, lyid, ryid);
    }
};

int main(){
    
    std::ifstream in("text.txt");
    std::cin.rdbuf(in.rdbuf());
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    int Q;cin>>Q;
    while(Q--){
        ll N,K;cin>>N>>K;
        vector<int> A(N);
        vector<ll> rui(N+1);
        for(int i=0;i<N;i++){
            cin>>A[i];
            A[i]+=N;
            A[i]-=i;
            rui[i+1]=rui[i]+A[i];
        }
        WaveletMatrix WM(A);
        
        ll left=1,right=N+1;
        while(right-left>1){
            ll mid=(left+right)/2;
            bool ok=false;
            
            for(ll l=0;l+mid<=N;l++){
                ll r=l+mid;
                ll x=WM.quantile(mid/2,l,r);
                ll need=0;
                ll Z=WM.topKsum(mid/2,l,r);
                need+=x*(mid/2)-Z;
                need+=(rui[r]-rui[l]-Z-x)-x*(mid-mid/2-1);
                if(need<=K){
                    ok=true;
                    break;
                }
            }
            
            if(ok) left=mid;
            else right=mid;
        }
        
        cout<<left<<"\n";
    }
}