Problem:
Score : 1100 points

Problem Statement

Let f(A, B), where A and B are positive integers, be the string satisfying the following conditions:

f(A, B) has length A + B;

f(A, B) contains exactly A letters A and exactly B letters B;

The length of the longest substring of f(A, B) consisting of equal letters (ex., AAAAA or BBBB) is as small as possible under the conditions above;

f(A, B) is the lexicographically smallest string satisfying the conditions above.

For example, f(2, 3) = BABAB, and f(6, 4) = AABAABAABB.

Answer Q queries: find the substring of f(A_i, B_i) from position C_i to position D_i (1-based).

Constraints

1 \leq Q \leq 10^3

1 \leq A_i, B_i \leq 5 \times 10^8

1 \leq C_i \leq D_i \leq A_i + B_i

D_i - C_i + 1 \leq 100

All input values are integers.

Partial Score

500 points will be awarded for passing the testset satisfying 1 \leq A_i, B_i \leq 10^3.

Input

Input is given from Standard Input in the following format:

Q
A_1 B_1 C_1 D_1
A_2 B_2 C_2 D_2
:
A_Q B_Q C_Q D_Q

Output

For each query i in order of input, print a line containing the substring of f(A_i, B_i) from position C_i to position D_i (1-based).

Sample Input 1

5
2 3 1 5
6 4 1 10
2 3 4 4
6 4 3 7
8 10 5 8

Sample Output 1

BABAB
AABAABAABB
A
BAABA
ABAB

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

#if 0
cat <<EOF >mistaken-paste
#endif
// thanks for @rsk0315_h4x

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"
#define _USE_MATH_DEFINES

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <time.h>

#define BIG 2000000007
#define VERYBIG 2000000000000007LL

#define MOD 1000000007
#define FOD  998244353
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 1000000

#ifdef __cplusplus
#include <queue>
#include <stack>
#include <tuple>
#include <set>
#include <map>
#include <string>
#include <algorithm>
#include <functional>
#include <array>

using std::queue;
using std::priority_queue;
using std::stack;
using std::tuple;
using std::set;
using std::map;
using std::vector;
using std::greater;
using std::pair;
using std::string;
using std::get;

template <typename T, typename U>
pair<T, U> operator+(pair<T, U> l, pair<T, U> r) {
	return pair<T, U>(l.first + r.first, l.second + r.second);
}

#endif

typedef struct {
	int32_t a;
	int32_t b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;

typedef struct {
	sll a;
	sll b;
	sll c;
} hwllc;

typedef struct {
	hwll a;
	hwll b;
} linell;

ull n, m;
ull h, w;
ull k;
ull q;
sll va, vb, vc, vd, ve, vf;
ull ua, ub, uc, ud, ue, uf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
char ch, dh;

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

ull divide (ull a, ull b, ull modulo) {
	return (a * bitpow(b, modulo - 2, modulo)) % modulo;
}

ull udiff (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sdiff (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

int bitcount (ull n) {
	int result = 0;
	while (n) {
		if (n & 1) result++;
		n /= 2;
	}
	return result;
}

#define BEGCMP(NAME) int32_t NAME (const void *left, const void *right)
#define DEFLR(TYPE) TYPE l=*(TYPE*)left,r=*(TYPE*)right
#define CMPRET(L, R) if((L)<(R))return-1;if((L)>(R))return+1

// int32_t pullcomp (const void *left, const void *right) {
// 	ull l = *(ull*)left;
// 	ull r = *(ull*)right;
// 	if (l < r) {
// 		return -1;
// 	}
// 	if (l > r) {
// 		return +1;
// 	}
// 	return 0;
// }
BEGCMP(pullcomp){
	DEFLR(ull);
	CMPRET(l, r);
	return 0;
}
BEGCMP(prevcomp){
	DEFLR(ull);
	CMPRET(r, l);
	return 0;
}
BEGCMP(psllcomp){
	DEFLR(sll);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pcharcomp){
	DEFLR(char);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pdoublecomp){
	DEFLR(double);
	CMPRET(l, r);
	return 0;
}

int32_t pstrcomp (const void *left, const void *right) {
	char* l = *(char**)left;
	char* r = *(char**)right;

	return strcmp(l, r);
}

BEGCMP(phwllABcomp){
	DEFLR(hwll);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}
BEGCMP(phwllREVcomp){
	DEFLR(hwll);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	return 0;
}
BEGCMP(ptriplecomp){
	DEFLR(hwllc);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	CMPRET(l.c, r.c);
	return 0;
}
BEGCMP(ptripleREVcomp){
	DEFLR(hwllc);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	CMPRET(l.c, r.c);
	return 0;
}

int32_t pquadcomp (const void *left, const void *right) {
	linell l = *(linell*)left;
	linell r = *(linell*)right;

	sll ac = phwllABcomp(&(l.a), &(r.a));
	if (ac) return ac;
	sll bc = phwllABcomp(&(l.b), &(r.b));
	if (bc) return bc;

	return 0;
}

bool isinrange (sll left, sll x, sll right) {
	return (left <= x && x <= right);
}

bool isinrange_soft (sll left, sll x, sll right) {
	return (left <= x && x <= right) || (left >= x && x >= right);
}

sll a[N_MAX + 5];
// ull a[N_MAX + 5];
// sll a[3001][3001];
sll b[N_MAX + 5];
// ull b[N_MAX + 5];
// sll b[3001][3001];
sll c[N_MAX + 5];
ull d[N_MAX + 5];
sll e[N_MAX];
char s[N_MAX + 1];
// char s[3010][3010];
char t[N_MAX + 1];
// char t[3010][3010];
char u[N_MAX + 1];
hwll xy[N_MAX + 5];
hwllc tup[N_MAX + 5];
sll table[3005][3005];
// here we go



ull solve () {
	sll i, j, ki, li;
	// ull result = 0;
	sll result = 0;
	double dresult = 0;
	// ull maybe = 0;
	sll maybe = 0;
	// ull sum = 0;
	sll sum = 0;
	sll item;
	ull *dpcell;

	while (q--) {
		scanf("%llu%llu%llu%llu", &ua, &ub, &uc, &ud);

		ull l = (umax(ua, ub) - 1) / (umin(ua, ub) + 1) + 1;
		if (l == 1) {
			for (i = uc; i <= ud; i++) {
				putchar(((i + ((ub > ua) ? 1 : 0)) % 2) ? 'A' : 'B');
			}
			puts("");
			continue;
		}
		ull befk;
		ull xa;
		ull xb;
		if (ua * l <= ub) {
			befk = 0;
		} else {
			befk = (ua * l - ub - 1) / (l * l - 1);
		}
		ull arem = ua - l * befk;
		ull brem = ub - befk;
		xa = arem - (brem - 1) / l;
		arem -= xa;
		xb = brem - l * arem;

		for (i = uc; i <= ud; i++) {
			bool isa;
			if (i <= befk * (l + 1) + xa) {
				if (i % (l + 1)) {
					isa = true;
				} else {
					isa = false;
				}
			} else {
				if ((ua + ub - i + 1) % (l + 1)) {
					isa = false;
				} else {
					isa = true;
				}
			}
			putchar(isa ? 'A' : 'B');
		}
		puts("");
	}

	// printf("%lld\n", result);
	// printf("%.15lf\n", dresult);
	// puts(s);

	return 0;

	success:
	puts("YES");
	// puts("Yes");
	// printf("%llu\n", result);
	// puts("0");
	// puts("Yay!");
	return 0;

	fail:
	// puts("NO");
	// puts("No");
	// puts("0");
	puts("-1");
	// puts("-1 -1 -1");
	// puts("Impossible");
	return 1;
}

int32_t main (void) {
	int32_t i, j;
	int32_t x, y;



	// scanf("%llu%llu", &h, &w);
	// scanf("%llu", &n, &m);
	// scanf("%llu", &k, &n, &m);
	// scanf("%llu%llu", &h, &w);
	scanf("%llu", &q);
	// scanf("%s", s);
	// scanf("%lld%lld", &va, &vb, &vc, &vd);
	// scanf("%llu%llu%llu", &ua, &ub, &uc, &ud);
	// scanf("%s", t);
	// scanf("%lld", &m);
	// for (i = 0; i < m; i++) {
	// 	// scanf("%lld%lld", &xy[i].a, &xy[i].b);
	// 	// scanf("%lld%lld%lld", &tup[i].a, &tup[i].b, &tup[i].c);
	// 	scanf("%lld", &a[i]);
	// 	scanf("%lld", &b[i]);
	// 	// scanf("%lld", &c[i]);
	// 	// scanf("%lld", &d[i]);
	// 	a[i]--;
	// 	b[i]--;
	// 	// c[i]--;
	// 	// d[i]--;
	// 	// xy[i].a--;
	// 	// xy[i].b--;
	// 	// tup[i].a--;
	// 	// tup[i].b--;
	// }
	// scanf("%llu", &m, &k);
	// scanf("%llu", &q);
	// scanf("%s", s);
	// for (i = 0; i < n; i++) {
	// 	scanf("%lld", &a[i]);
	// 	// scanf("%lld", &b[i]);
	// 	// b[i]--;
	// 	// c[i]--;
	// }
	// scanf("%llu", &q);

	// for (i = 0; i < q; i++) {
	// 	scanf("%lld%lld", &xy[i].a, &xy[i].b);
	// 	xy[i].a--;
	// 	xy[i].b--;
	// }

	// for (i = 0; i < n; i++) {
	// 	for (j = 0; j < n; j++) {
	// 		scanf("%lld", &table[i][j]);
	// 		// table[i][j]--;
	// 	}
	// }
	// for (i = 0; i < h; i++) {
	// 	scanf("%s", s[i]);
	// }
	// scanf("%llu", &q);

	solve();

	return 0;
}