Problem:
Score : 600 points

Problem Statement

Ringo Mart, a convenience store, sells apple juice.

On the opening day of Ringo Mart, there were A cans of juice in stock in the morning.
Snuke buys B cans of juice here every day in the daytime.
Then, the manager checks the number of cans of juice remaining in stock every night.
If there are C or less cans, D new cans will be added to the stock by the next morning.

Determine if Snuke can buy juice indefinitely, that is, there is always B or more cans of juice in stock when he attempts to buy them.
Nobody besides Snuke buy juice at this store.

Note that each test case in this problem consists of T queries.

Constraints

1 \leq T \leq 300

1 \leq A, B, C, D \leq 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

T
A_1 B_1 C_1 D_1
A_2 B_2 C_2 D_2
:
A_T B_T C_T D_T

In the i-th query, A = A_i, B = B_i, C = C_i, D = D_i.

Output

Print T lines. The i-th line should contain Yes if Snuke can buy apple juice indefinitely in the i-th query; No otherwise.

Sample Input 1

14
9 7 5 9
9 7 6 9
14 10 7 12
14 10 8 12
14 10 9 12
14 10 7 11
14 10 8 11
14 10 9 11
9 10 5 10
10 10 5 10
11 10 5 10
16 10 5 10
1000000000000000000 17 14 999999999999999985
1000000000000000000 17 15 999999999999999985

Sample Output 1

No
Yes
No
Yes
Yes
No
No
Yes
No
Yes
Yes
No
No
Yes

In the first query, the number of cans of juice in stock changes as follows: (D represents daytime and N represents night.)

9
→D 2
→N 11
→D 4
→N 13
→D 6
→N 6
→D x

In the second query, the number of cans of juice in stock changes as follows:

9
→D 2
→N 11
→D 4
→N 13
→D 6
→N 15
→D 8
→N 8
→D 1
→N 10
→D 3
→N 12
→D 5
→N 14
→D 7
→N 7
→D 0
→N 9
→D 2
→N 11
→D …

and so on, thus Snuke can buy juice indefinitely.

Sample Input 2

24
1 2 3 4
1 2 4 3
1 3 2 4
1 3 4 2
1 4 2 3
1 4 3 2
2 1 3 4
2 1 4 3
2 3 1 4
2 3 4 1
2 4 1 3
2 4 3 1
3 1 2 4
3 1 4 2
3 2 1 4
3 2 4 1
3 4 1 2
3 4 2 1
4 1 2 3
4 1 3 2
4 2 1 3
4 2 3 1
4 3 1 2
4 3 2 1

Sample Output 2

No
No
No
No
No
No
Yes
Yes
No
No
No
No
Yes
Yes
Yes
No
No
No
Yes
Yes
Yes
No
No
No

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
#ifndef LOCAL
#pragma comment(linker, "/STACK:167772160")
#endif

using namespace std;

#ifdef LOCAL

template <typename T, typename Q>
ostream& operator<<(ostream& os, pair<T, Q> p)
{
	return (os << '(' << p.first << ", " << p.second << ')');
}

int _iterable_indent = 0;
template<class T>
std::ostream& print_iterable(std::ostream& os, T beg, T end)
{
	if (_iterable_indent > 0)
		os << "\n";
	for (int i = 0; i < _iterable_indent; ++i)
		os << "\t";
	os << "[";
	for (auto it = beg; it != end; ++it)
	{
		if (it != beg)
			os << ", ";
		++_iterable_indent;
		os << *it;
		--_iterable_indent;
	}
	os << "]";
	return os;
}

template <class T >
std::ostream& operator << (std::ostream& os, const std::vector<T>& v)
{
	return print_iterable(os, v.begin(), v.end());
}
template <class T >
std::ostream& operator << (std::ostream& os, const std::set<T>& v)
{
	return print_iterable(os, v.begin(), v.end());
}
template <class T >
std::ostream& operator << (std::ostream& os, const std::multiset<T>& v)
{
	return print_iterable(os, v.begin(), v.end());
}
template <class T >
std::ostream& operator << (std::ostream& os, const std::unordered_set<T>& v)
{
	return print_iterable(os, v.begin(), v.end());
}
template <class T, class Q>
std::ostream& operator << (std::ostream& os, const std::map<T, Q>& v)
{
	return print_iterable(os, v.begin(), v.end());
}
template <class T, class Q>
std::ostream& operator << (std::ostream& os, const std::unordered_map<T, Q>& v)
{
	return print_iterable(os, v.begin(), v.end());
}

vector<string> _split(const string& s, char c) {
	vector<string> v;
	stringstream ss(s);
	string x;
	auto arr_skip = false;
	while (getline(ss, x, c))
	{
		while (x[0] == ' ')
			x = x.substr(1);
		if (arr_skip)
		{
			for (auto h : x)
				if (h == ')')
					arr_skip = false;
			continue;
		}
		if (x.size() >= 3 && x.substr(0, 3) == "ARR")
		{
			arr_skip = true;
			v.emplace_back(x.substr(4));
		}
		else
			v.emplace_back(x);
	}
	return v;
}

void _print(vector<string>::iterator) {}
template<typename T, typename... Args>
void _print(vector<string>::iterator it, T a, Args... args) {
	string name = it->substr((*it)[0] == ' ', it->length());
	if (isalpha(name[0]))
		cerr << name << " = " << a << endl;
	else
		cerr << name << endl;
	_print(++it, args...);
}

template<class T>
auto _kekeke(T x)
{
	return x;
}

template<class T>
auto make_vector(T arr)
{
	return arr;
}

template<class T, class... Args>
auto make_vector(T arr, int len, Args... args)
{
	auto inside = make_vector(arr[0], args...);
	vector<decltype(_kekeke(inside))> v;
	for (int i = 0; i < len; ++i)
		v.push_back(make_vector(arr[i], args...));
	return v;
}

#define dbg(...) { _print(_split(#__VA_ARGS__, ',').begin(), __VA_ARGS__); }
#define ARR(arr, ...) make_vector(arr, __VA_ARGS__)
#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
#define dbg(...) (void)0
#define ARR(arr, ...) (void)0
#define eprintf(...) (void)0
#endif
#define mp make_pair
#define rand govno_ebanoe
#define dbg_time() eprintf("\n\nTime: %.3lf\n", double(clock()) / CLOCKS_PER_SEC)

using ll = long long;
using ull = unsigned long long;
using uint = unsigned int;
using pii = pair<int, int>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
using dbl = double;

const int INF = (int)1e9 + 10;
const ll LINF = ll(2e18) + 10;
const double PI = acosl(-1);
const double eps = 1e-8;

#define MULTITEST

ll gcd(ll a, ll b)
{
    while(b) {
        a %= b;
        swap(a, b);
    }
    return a;
}

void solve()
{
    ll a, b, c, d;
    scanf("%lld%lld%lld%lld", &a, &b, &c, &d);
    if (b > a || b > d)
    {
        puts("No");
        return;
    }
    if (b <= c + 1)
    {
        puts("Yes");
        return;
    }
    auto g = gcd(b, d);
    auto r = a % g + g * (c / g);
    if (r <= c)
        r += g;
    puts(r < b ? "No" : "Yes");
}

#ifdef LOCAL
#define ERR_CATCH
//#define NOERR
#endif

int main()
{
#ifdef LOCAL
	freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);
#ifdef NOERR
	freopen("err.txt", "w", stderr);
#endif
#else
	//freopen("sum.in", "r", stdin);
	//freopen("sum.out", "w", stdout);
#endif

#ifdef ERR_CATCH
	try
	{
#endif

#ifdef ST
		ios_base::sync_with_stdio(false);
		while (true)
			solve();
#endif

#ifdef CASES
#define MULTITEST
#endif

#ifdef MULTITEST
		int t;
		scanf("%d", &t);
		char endl1[5];
		fgets(endl1, 5, stdin);
		for (int i = 0; i < t; ++i)
		{
#ifdef CASES
			printf("Case #%d: ", i + 1);
#endif
			solve();
#ifdef CASES
			eprintf("Passed case #%d:\n", i + 1);
#endif
		}
#else
		solve();
#endif

#ifdef ERR_CATCH
	}
	catch (logic_error e)
	{
		dbg(e.what());
		puts("___________________________________________________________________________");
		exit(0);
	}
#endif
	dbg_time();
}