#include <iostream>
#include <numeric>
#include <ranges>
#include <algorithm>
#include <vector>
#include <cassert>
using namespace std;
using ll=long long;
int main(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	int ttt;
	cin>>ttt;
	assert(1<=ttt&&ttt<=200000);
	ll sum=0;
	while(ttt--){
		int n;
		cin>>n;
		assert(1<=n&&n<=200000);
		sum+=n;
		vector<int> a(n);
		for(int i=0;i<n;i++){
			cin>>a[i];
			assert(0<=a[i]&&a[i]<=1000000000);
		}
		if(n==1){
			cout<<max(a[0],1)<<endl;
			return 0;
		}
		vector<int> cnt(n);
		for(int i=0;i<n;i++){
			if(a[i]>=n)cnt[0]++;
			else cnt[a[i]]++;
		}
		int l=0,r=n+1;
		while(l+1<r){
			int c=(l+r)/2;
			ll need=1;
			vector<int> b=cnt;
			for(int i=c;i<n;i++)b[0]+=b[i];
			for(int i=c-1;i>=1;i--){
				if(b[i]>=need){
					b[0]+=b[i]-need;
				}else{
					need+=(need-b[i]);
				}
				if(need>n)break;
			}
			if(need<=b[0])l=c;
			else r=c;
		}
		cout<<l<<endl;
	}
	assert(sum<=200000);
}