1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define vc vector
#define st first
#define nd second
#define pll pair<ll, ll>
#define sz(a) (ll)a.size()
#define all(a) a.begin(), a.end()
#define pu push
#define pub push_back
#define pob pop_back
#define em emplace
#define emb emplace_back
const ll INF = 2e18;
const ll B = 50'000'000;
ll R = 183;

ll n, m;
vc<ll> a;

void input() {
	cin >> n;
	a.resize(n);
	for (ll &ai : a)
		cin >> ai;
}

ll ceil(ll x, ll y) {
	return (x + y - 1) / y;
}

bool check() {
	ll p = 0;
	R = 183;
	for (ll x = 1; x <= 200; x++) {
		ll w = x * (x - 1) * (x - 2) / 6;
		w += x * (x - 1) / 2 * (m - x);
		if (w >= 1'000'000 or w < 0) {
			R = x;
			break;
		}
	}
	for (ll i = 0; i < n; i++) {
		if (a[i] == 0)
			continue;
		if (i == 0) {
			for (ll x = 1; x <= R + 1; x++) {
				if (x == R + 1)
					return false;
				ll w = x * (x - 1) * (x - 2) / 6;
				w += x * (x - 1) / 2 * (m - x);
				if (w >= a[i]) {
					p = x;
					break;
				}
			}
			if (p > m)
				return false;
			continue;
		}
		if (i == n - 1) {
			for (ll x = 1; x <= R + 1; x++) {
				if (x == R + 1)
					return false;
				ll w = x * (x - 1) * (x - 2) / 6;
				w += x * (x - 1) / 2 * (m - x);
				if (w >= a[i]) {
					p += x;
					break;
				}
			}
			if (p > m)
				return false;
			continue;
		}
		ll np = INF;
		for (ll x = 1; x <= R; x++) {
			ll w = x * (x - 1) * (x - 2) / 6;
			w += x * (x - 1) / 2 * (m - x);
			ll l = p, r = max((m - x) / 2, p) + 1;
			while (l < r) {
				ll s = (l + r) / 2;
				if (w + s * x * (m - x - s) >= a[i])
					r = s;
				else
					l = s + 1;
			}
			if (l > max((m - x) / 2, p))
				continue;
			np = min(np, l + x);
		}
		if (np > m)
			return false;
		p = np;
	}
	return true;
}

ll binsearch() {
	if (n == 1) {
		for (ll x = 1; x <= R; x++) {
			if (x * (x - 1) * (x - 2) / 6 >= a[0])
				return x;
		}
	}
	ll pos = 0;
	for (ll &ai : a)
		if (ai > 0)
			pos++;
	ll l = pos, r = B;
	while (l < r) {
		m = (l + r) / 2;
		if (check())
			r = m;
		else
			l = m + 1;
	}
	return l;
}

void program() {
	input();
	cout << binsearch() << "\n";
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);
	cout.tie(nullptr);
	ll T = 1;
	cin >> T;
	while (T--)
		program();
	return 0;
}