G - Batman Mex

#include <bits/stdc++.h>

using namespace std;

#define cin_2d(vec, n, m) for(int i = 0; i < n; i++) for(int j = 0; j < m && cin >> vec[i][j]; j++);
#define cout_2d(vec, n, m) for(int i = 0; i < n; i++, cout << "\n") for(int j = 0; j < m && cout << vec[i][j] << " "; j++);
#define fixed(n) fixed << setprecision(n)
#define ceil(n, m) (((n) / (m)) + ((n) % (m) ? 1 : 0))
#define fill(vec, value) memset(vec, value, sizeof(vec));
#define mul_mod(a, b, m) (((a % m) * (b % m)) % m)
#define add_mod(a, b, m) (((a % m) + (b % m)) % m)
#define all(vec) vec.begin(), vec.end()
#define rall(vec) vec.rbegin(), vec.rend()
#define sz(x) int(x.size())
#define debug(x) cout << #x << ": " << (x) << "\n";
#define fi first
#define se second
#define ll long long
#define ull unsigned long long
#define Mod  1'000'000'007
#define OO 2'000'000'000
#define EPS 1e-9
#define PI acos(-1)
template < typename T = int > using Pair = pair < T, T >;
vector < string > RET = {"NO", "YES"};

template < typename T = int > istream& operator >> (istream &in, vector < T > &v) {
    for (auto &x : v) in >> x;
    return in;
}

template < typename T = int > ostream& operator << (ostream &out, const vector < T > &v) {
    for (const T &x : v) out << x << ' ';
    return out;
}

ll sum(ll n){
    return n * (n - 1) / 2;
}

void Solve(){
    ll n, k;
    cin >> n >> k;
    vector < ll > nums(n), idx(n + 1, n + 1), freq(n + 1);
    cin >> nums;
    for(int i = 0; i < n; i++)
        idx[nums[i]] = i + 1;
    ll max_r = idx[0], min_l = idx[0];
    freq[0] += sum(idx[0]) + sum(n - idx[0] + 1);
    for(int i = 1; i <= n; i++){
        max_r = max(max_r, idx[i - 1]);
        min_l = min(min_l, idx[i - 1]);
        if(max_r < idx[i])
            freq[i] += (min_l * (idx[i] - max_r));
        else if(min_l > idx[i])
            freq[i] += ((min_l - idx[i]) * (n - max_r + 1));
    }
    for(int i = 0; i <= n; i++){
        if(freq[i] < k)
            k -= freq[i];
        else
            return cout << i << "\n", void();
    }
}


int main(){
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    int t = 1;
    cin >> t;
    while(t--)
        Solve();
    return 0;
}