Problem p03466 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>

//    #include <boost/multiprecision/cpp_int.hpp>
#define int long long
#define inf 1000000007
#define pa pair<int, int>
#define ll long long
#define pal pair<double, double>
#define ppap pair<pa, int>
#define PI 3.14159265358979323846
#define paa pair<int, char>
#define mp make_pair
#define pb push_back
#define EPS (1e-10)

int dx[8] = {0, 1, 0, -1, 1, 1, -1, -1};
int dy[8] = {1, 0, -1, 0, -1, 1, 1, -1};
using namespace std;
class pa3 {
public:
  int x;
  int y, z;
  pa3(int x = 0, int y = 0, int z = 0) : x(x), y(y), z(z) {}
  bool operator<(const pa3 &p) const {
    if (x != p.x)
      return x < p.x;
    if (y != p.y)
      return y < p.y;
    return z < p.z;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator>(const pa3 &p) const {
    if (x != p.x)
      return x > p.x;
    if (y != p.y)
      return y > p.y;
    return z > p.z;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator==(const pa3 &p) const {
    return x == p.x && y == p.y && z == p.z;
  }
  bool operator!=(const pa3 &p) const {
    return !(x == p.x && y == p.y && z == p.z);
  }
};

class pa4 {
public:
  int x;
  int y, z, w;
  pa4(int x = 0, int y = 0, int z = 0, int w = 0) : x(x), y(y), z(z), w(w) {}
  bool operator<(const pa4 &p) const {
    if (x != p.x)
      return x < p.x;
    if (y != p.y)
      return y < p.y;
    if (z != p.z)
      return z < p.z;
    return w < p.w;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator>(const pa4 &p) const {
    if (x != p.x)
      return x > p.x;
    if (y != p.y)
      return y > p.y;
    if (z != p.z)
      return z > p.z;
    return w > p.w;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator==(const pa4 &p) const {
    return x == p.x && y == p.y && z == p.z && w == p.w;
  }
};
class pa2 {
public:
  int x, y;
  pa2(int x = 0, int y = 0) : x(x), y(y) {}
  pa2 operator+(pa2 p) { return pa2(x + p.x, y + p.y); }
  pa2 operator-(pa2 p) { return pa2(x - p.x, y - p.y); }
  bool operator<(const pa2 &p) const { return y != p.y ? y < p.y : x < p.x; }
  bool operator>(const pa2 &p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator==(const pa2 &p) const {
    return abs(x - p.x) == 0 && abs(y - p.y) == 0;
  }
  bool operator!=(const pa2 &p) const {
    return !(abs(x - p.x) == 0 && abs(y - p.y) == 0);
  }
};

class Point {
public:
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(Point p) { return Point(x - p.x, y - p.y); }
  Point operator*(double a) { return Point(x * a, y * a); }
  Point operator/(double a) { return Point(x / a, y / a); }
  double absv() { return sqrt(norm()); }
  double norm() { return x * x + y * y; }
  bool operator<(const Point &p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator==(const Point &p) const {
    return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
  }
};
typedef Point Vector;
#define pl pair<int, pas>
struct Segment {
  Point p1, p2;
};
double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; }
double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

bool parareru(Point a, Point b, Point c, Point d) {
  //	if(abs(cross(a-b,d-c))<EPS)cout<<"dd "<<cross(a-b,d-c)<<endl;
  return abs(cross(a - b, d - c)) < EPS;
}
double distance_ls_p(Point a, Point b, Point c) {
  if (dot(b - a, c - a) < EPS)
    return (c - a).absv();
  if (dot(a - b, c - b) < EPS)
    return (c - b).absv();
  return abs(cross(b - a, c - a)) / (b - a).absv();
}
bool is_intersected_ls(Segment a, Segment b) {
  if (a.p1 == b.p1 || a.p2 == b.p1 || a.p1 == b.p2 || a.p2 == b.p2)
    return false;
  if (parareru((a.p2), (a.p1), (a.p1), (b.p2)) &&
      parareru((a.p2), (a.p1), (a.p1), (b.p1))) {
    //		cout<<"sss"<<endl;
    if (dot(a.p1 - b.p1, a.p1 - b.p2) < EPS)
      return true;
    if (dot(a.p2 - b.p1, a.p2 - b.p2) < EPS)
      return true;
    if (dot(a.p1 - b.p1, a.p2 - b.p1) < EPS)
      return true;
    if (dot(a.p1 - b.p2, a.p2 - b.p2) < EPS)
      return true;
    return false;
  } else
    return (cross(a.p2 - a.p1, b.p1 - a.p1) * cross(a.p2 - a.p1, b.p2 - a.p1) <
            EPS) &&
           (cross(b.p2 - b.p1, a.p1 - b.p1) * cross(b.p2 - b.p1, a.p2 - b.p1) <
            EPS);
}

double segment_dis(Segment a, Segment b) {
  if (is_intersected_ls(a, b))
    return 0;
  double r = distance_ls_p(a.p1, a.p2, b.p1);
  r = min(r, distance_ls_p(a.p1, a.p2, b.p2));
  r = min(r, distance_ls_p(b.p1, b.p2, a.p2));
  r = min(r, distance_ls_p(b.p1, b.p2, a.p1));
  return r;
}
Point intersection_ls(Segment a, Segment b) {
  Point ba = b.p2 - b.p1;
  double d1 = abs(cross(ba, a.p1 - b.p1));
  double d2 = abs(cross(ba, a.p2 - b.p1));
  double t = d1 / (d1 + d2);

  return a.p1 + (a.p2 - a.p1) * t;
}

string itos(int i) {
  ostringstream s;
  s << i;
  return s.str();
}

int gcd(int v, int b) {
  if (v > b)
    return gcd(b, v);
  if (v == b)
    return b;
  if (b % v == 0)
    return v;
  return gcd(v, b % v);
}

double distans(double x1, double y1, double x2, double y2) {
  double rr = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
  return sqrt(rr);
}
int mod;
ll extgcd(ll a, ll b, ll &x, ll &y) {
  if (b == 0ll) {
    x = 1ll;
    y = 0ll;
    return a;
  }
  ll d = extgcd(b, a % b, y, x);
  y -= a / b * x;
  return d;
}
pa operator+(const pa &l, const pa &r) {
  return {l.first + r.first, l.second + r.second};
}
pa operator-(const pa &l, const pa &r) {
  return {l.first - r.first, l.second - r.second};
}

int pr[1200010];
int inv[1200010];

int beki(int wa, int rr, int warukazu) {
  if (rr == 0)
    return 1 % warukazu;
  if (rr == 1)
    return wa % warukazu;
  wa %= warukazu;
  if (rr % 2 == 1)
    return ((ll)beki(wa, rr - 1, warukazu) * (ll)wa) % warukazu;
  ll zx = beki(wa, rr / 2, warukazu);
  return (zx * zx) % warukazu;
}
double bekid(double w, int r) {
  if (r == 0)
    return 1.0;
  if (r == 1)
    return w;
  if (r % 2)
    return bekid(w, r - 1) * w;
  double f = bekid(w, r / 2);
  return f * f;
}

int comb(int nn, int rr) {
  int r = pr[nn] * inv[rr];
  r %= mod;
  r *= inv[nn - rr];
  r %= mod;
  return r;
}

void gya(int ert) {
  pr[0] = 1;
  for (int i = 1; i <= ert; i++) {
    pr[i] = (pr[i - 1] * i) % mod;
  }
  for (int i = 0; i <= ert; i++)
    inv[i] = beki(pr[i], mod - 2, mod);
}

//   cin.tie(0);
//	ios::sync_with_stdio(false);
// priority_queue<pa3,vector<pa3>,greater<pa3>> pq;
// sort(ve.begin(),ve.end(),greater<int>());
// mt19937(clock_per_sec);
//  mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()) ;

//----------------kokomade tenpure------------

string solve_gu(int a, int b) {
  vector<int> ve;
  for (int i = 0; i < a; i++)
    ve.pb(0);
  for (int i = 0; i < b; i++)
    ve.pb(1);

  pair<int, vector<int>> g;
  g.first = inf;

  do {
    int ma = 1;
    int len = 1;
    for (int i = 0; i < a + b; i++) {
      if (i) {
        if (ve[i - 1] != ve[i]) {
          ma = max(ma, len);
          len = 1;
        } else
          len++;
        if (len > g.first)
          goto lll;
      }
    }
    ma = max(ma, len);

    g = min(g, mp(ma, ve));
  lll:;

  } while (next_permutation(ve.begin(), ve.end()));
  string st = "";
  for (auto c : g.second)
    st += (c ? "1" : "0");
  return st;
}

string solve(int a, int b, int c, int d) {
  assert(a >= b);
  //	cout<<a<<" "<<b<<" "<<c<<" "<<d<<endl;
  string ans = "";
  assert(a <= 1010 && b <= 1010);
  if (a == b) {
    for (int i = c; i < d; i++) {
      if (i % 2)
        ans += "1";
      else
        ans += "0";
    }
    return ans;
  }

  if (a == b + 1) {
    for (int i = c; i < d; i++) {
      if (i % 2)
        ans += "1";
      else
        ans += "0";
    }
    return ans;
  }

  int x = (a / (b + 1) + !!(a % (b + 1)));

  //	int aa=(b+1)*(a/(b+1)+!!(a%(b+1)));

  // cout<<x<<" "<<aa<<endl;

  if (a >= x * b) {
    for (int i = c; i < d; i++) {
      if (i % (x + 1) == x)
        ans += "1";
      else
        ans += "0";
    }
    return ans;
  }
  /*
  int nokori=x*b-a;
  string tani="";
  for(int i=0;i<x;i++)tani+="0";
  tani+="1";
  string s="";
  for(int i=0;i<b;i++)s+=tani;

  vector<int> ve;
  assert(s.length()==b*(x+1));
  ve.resize((int)s.length(),0);
  for(int i=0;i<b*(x+1);i++){
          if(s[i]=='1')ve[i]=1;
  }
  int cnt=1;
  for(int ima=b*(x);ima>=0;ima-=x+1){
          if(cnt%x==0)ve[ima]=1;
          cnt++;
  }
  for(int i=b*(x+1)-1;;i--)if(ve[i]==0){
          ve[i]=-1;
          nokori--;
          if(nokori==0) break;
  }
  cnt=0;
  for(int i=0;;i++)if(ve[i]>=0){
          if(c<=cnt && cnt<d){
                  ans+=s[i];
                  if(cnt==d-1)break;
          }
                  cnt++;

  }
  */
  // cout<<a<<" "<<b<<" "<<c<<" "<<d<<endl;
  swap(c, d);
  c = a + b - c;
  d = a + b - d;
  //	cout<<c<<" "<<d<<endl;
  int nokori = x * b - a;
  //	cout<<nokori<<endl;
  int d1 = nokori / (x * x - 1);
  // di 1--(x)個--10
  // (x+1)*d1文字
  //	cout<<"d1 "<<d1<<endl;
  nokori %= x * x - 1;
  int d2 = nokori / x;
  // d2は長さ 1----1
  // d2文字
  //	cout<<"d2 "<<d2<<endl;
  nokori %= x;

  int d3 = x - nokori;
  //	cout<<"d3 "<<d3<<endl;

  // 10-(d3)-0
  // d3+1文字

  for (int i = c; i < d; i++) {
    if ((x + 1) * d1 > i) {
      int ii = i % (x + 1);
      if (ii == x)
        ans += "0";
      else
        ans += "1";
    } else if ((x + 1) * d1 + d2 > i) {
      ans += "1";
    } else if ((x + 1) * d1 + d2 + d3 + 1 > i) {
      if (i == (x + 1) * d1 + d2)
        ans += "1";
      else
        ans += "0";
    } else {
      int ii = i - ((x + 1) * d1 + d2 + d3 + 1);
      ii %= x + 1;
      if (ii == 0)
        ans += "1";
      else
        ans += "0";
    }
  }

  // cout<<ans<<endl;

  reverse(ans.begin(), ans.end());
  return ans;
}

signed main() {

  cin.tie(0);
  ios::sync_with_stdio(false);
  //	cout<<solve_gu(8,10)<<endl;
  //	cout<<solve_gu(10,8)<<endl;
  //	return 0;
  //	cout<<solve(6,3,0,9)<<endl;
  //	for(int i=10;i<=60;i++)cout<<solve(i,10,0,10+i)<<endl;
  //	return 0;
  int q;
  cin >> q;
  for (int i = 0; i < q; i++) {
    int a, b, c, d;
    cin >> a >> b >> c >> d;
    c--;

    string s;
    if (a >= b) {
      s = solve(a, b, c, d);
      for (auto c : s) {
        if (c == '0')
          cout << 'A';
        else
          cout << 'B';
      }
    } else {
      s = solve(b, a, a + b - d, a + b - c);
      reverse(s.begin(), s.end());
      for (auto c : s) {
        if (c == '1')
          cout << 'A';
        else
          cout << 'B';
      }
    }

    cout << "\n";
  }
  return 0;
}

Fixed submission:
#include <bits/stdc++.h>

//    #include <boost/multiprecision/cpp_int.hpp>
#define int long long
#define inf 1000000007
#define pa pair<int, int>
#define ll long long
#define pal pair<double, double>
#define ppap pair<pa, int>
#define PI 3.14159265358979323846
#define paa pair<int, char>
#define mp make_pair
#define pb push_back
#define EPS (1e-10)

int dx[8] = {0, 1, 0, -1, 1, 1, -1, -1};
int dy[8] = {1, 0, -1, 0, -1, 1, 1, -1};
using namespace std;
class pa3 {
public:
  int x;
  int y, z;
  pa3(int x = 0, int y = 0, int z = 0) : x(x), y(y), z(z) {}
  bool operator<(const pa3 &p) const {
    if (x != p.x)
      return x < p.x;
    if (y != p.y)
      return y < p.y;
    return z < p.z;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator>(const pa3 &p) const {
    if (x != p.x)
      return x > p.x;
    if (y != p.y)
      return y > p.y;
    return z > p.z;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator==(const pa3 &p) const {
    return x == p.x && y == p.y && z == p.z;
  }
  bool operator!=(const pa3 &p) const {
    return !(x == p.x && y == p.y && z == p.z);
  }
};

class pa4 {
public:
  int x;
  int y, z, w;
  pa4(int x = 0, int y = 0, int z = 0, int w = 0) : x(x), y(y), z(z), w(w) {}
  bool operator<(const pa4 &p) const {
    if (x != p.x)
      return x < p.x;
    if (y != p.y)
      return y < p.y;
    if (z != p.z)
      return z < p.z;
    return w < p.w;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator>(const pa4 &p) const {
    if (x != p.x)
      return x > p.x;
    if (y != p.y)
      return y > p.y;
    if (z != p.z)
      return z > p.z;
    return w > p.w;
    // return x != p.x ? x<p.x: y<p.y;
  }
  bool operator==(const pa4 &p) const {
    return x == p.x && y == p.y && z == p.z && w == p.w;
  }
};
class pa2 {
public:
  int x, y;
  pa2(int x = 0, int y = 0) : x(x), y(y) {}
  pa2 operator+(pa2 p) { return pa2(x + p.x, y + p.y); }
  pa2 operator-(pa2 p) { return pa2(x - p.x, y - p.y); }
  bool operator<(const pa2 &p) const { return y != p.y ? y < p.y : x < p.x; }
  bool operator>(const pa2 &p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator==(const pa2 &p) const {
    return abs(x - p.x) == 0 && abs(y - p.y) == 0;
  }
  bool operator!=(const pa2 &p) const {
    return !(abs(x - p.x) == 0 && abs(y - p.y) == 0);
  }
};

class Point {
public:
  double x, y;
  Point(double x = 0, double y = 0) : x(x), y(y) {}
  Point operator+(Point p) { return Point(x + p.x, y + p.y); }
  Point operator-(Point p) { return Point(x - p.x, y - p.y); }
  Point operator*(double a) { return Point(x * a, y * a); }
  Point operator/(double a) { return Point(x / a, y / a); }
  double absv() { return sqrt(norm()); }
  double norm() { return x * x + y * y; }
  bool operator<(const Point &p) const { return x != p.x ? x < p.x : y < p.y; }
  bool operator==(const Point &p) const {
    return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;
  }
};
typedef Point Vector;
#define pl pair<int, pas>
struct Segment {
  Point p1, p2;
};
double dot(Vector a, Vector b) { return a.x * b.x + a.y * b.y; }
double cross(Vector a, Vector b) { return a.x * b.y - a.y * b.x; }

bool parareru(Point a, Point b, Point c, Point d) {
  //	if(abs(cross(a-b,d-c))<EPS)cout<<"dd "<<cross(a-b,d-c)<<endl;
  return abs(cross(a - b, d - c)) < EPS;
}
double distance_ls_p(Point a, Point b, Point c) {
  if (dot(b - a, c - a) < EPS)
    return (c - a).absv();
  if (dot(a - b, c - b) < EPS)
    return (c - b).absv();
  return abs(cross(b - a, c - a)) / (b - a).absv();
}
bool is_intersected_ls(Segment a, Segment b) {
  if (a.p1 == b.p1 || a.p2 == b.p1 || a.p1 == b.p2 || a.p2 == b.p2)
    return false;
  if (parareru((a.p2), (a.p1), (a.p1), (b.p2)) &&
      parareru((a.p2), (a.p1), (a.p1), (b.p1))) {
    //		cout<<"sss"<<endl;
    if (dot(a.p1 - b.p1, a.p1 - b.p2) < EPS)
      return true;
    if (dot(a.p2 - b.p1, a.p2 - b.p2) < EPS)
      return true;
    if (dot(a.p1 - b.p1, a.p2 - b.p1) < EPS)
      return true;
    if (dot(a.p1 - b.p2, a.p2 - b.p2) < EPS)
      return true;
    return false;
  } else
    return (cross(a.p2 - a.p1, b.p1 - a.p1) * cross(a.p2 - a.p1, b.p2 - a.p1) <
            EPS) &&
           (cross(b.p2 - b.p1, a.p1 - b.p1) * cross(b.p2 - b.p1, a.p2 - b.p1) <
            EPS);
}

double segment_dis(Segment a, Segment b) {
  if (is_intersected_ls(a, b))
    return 0;
  double r = distance_ls_p(a.p1, a.p2, b.p1);
  r = min(r, distance_ls_p(a.p1, a.p2, b.p2));
  r = min(r, distance_ls_p(b.p1, b.p2, a.p2));
  r = min(r, distance_ls_p(b.p1, b.p2, a.p1));
  return r;
}
Point intersection_ls(Segment a, Segment b) {
  Point ba = b.p2 - b.p1;
  double d1 = abs(cross(ba, a.p1 - b.p1));
  double d2 = abs(cross(ba, a.p2 - b.p1));
  double t = d1 / (d1 + d2);

  return a.p1 + (a.p2 - a.p1) * t;
}

string itos(int i) {
  ostringstream s;
  s << i;
  return s.str();
}

int gcd(int v, int b) {
  if (v > b)
    return gcd(b, v);
  if (v == b)
    return b;
  if (b % v == 0)
    return v;
  return gcd(v, b % v);
}

double distans(double x1, double y1, double x2, double y2) {
  double rr = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
  return sqrt(rr);
}
int mod;
ll extgcd(ll a, ll b, ll &x, ll &y) {
  if (b == 0ll) {
    x = 1ll;
    y = 0ll;
    return a;
  }
  ll d = extgcd(b, a % b, y, x);
  y -= a / b * x;
  return d;
}
pa operator+(const pa &l, const pa &r) {
  return {l.first + r.first, l.second + r.second};
}
pa operator-(const pa &l, const pa &r) {
  return {l.first - r.first, l.second - r.second};
}

int pr[1200010];
int inv[1200010];

int beki(int wa, int rr, int warukazu) {
  if (rr == 0)
    return 1 % warukazu;
  if (rr == 1)
    return wa % warukazu;
  wa %= warukazu;
  if (rr % 2 == 1)
    return ((ll)beki(wa, rr - 1, warukazu) * (ll)wa) % warukazu;
  ll zx = beki(wa, rr / 2, warukazu);
  return (zx * zx) % warukazu;
}
double bekid(double w, int r) {
  if (r == 0)
    return 1.0;
  if (r == 1)
    return w;
  if (r % 2)
    return bekid(w, r - 1) * w;
  double f = bekid(w, r / 2);
  return f * f;
}

int comb(int nn, int rr) {
  int r = pr[nn] * inv[rr];
  r %= mod;
  r *= inv[nn - rr];
  r %= mod;
  return r;
}

void gya(int ert) {
  pr[0] = 1;
  for (int i = 1; i <= ert; i++) {
    pr[i] = (pr[i - 1] * i) % mod;
  }
  for (int i = 0; i <= ert; i++)
    inv[i] = beki(pr[i], mod - 2, mod);
}

//   cin.tie(0);
//	ios::sync_with_stdio(false);
// priority_queue<pa3,vector<pa3>,greater<pa3>> pq;
// sort(ve.begin(),ve.end(),greater<int>());
// mt19937(clock_per_sec);
//  mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()) ;

//----------------kokomade tenpure------------

string solve_gu(int a, int b) {
  vector<int> ve;
  for (int i = 0; i < a; i++)
    ve.pb(0);
  for (int i = 0; i < b; i++)
    ve.pb(1);

  pair<int, vector<int>> g;
  g.first = inf;

  do {
    int ma = 1;
    int len = 1;
    for (int i = 0; i < a + b; i++) {
      if (i) {
        if (ve[i - 1] != ve[i]) {
          ma = max(ma, len);
          len = 1;
        } else
          len++;
        if (len > g.first)
          goto lll;
      }
    }
    ma = max(ma, len);

    g = min(g, mp(ma, ve));
  lll:;

  } while (next_permutation(ve.begin(), ve.end()));
  string st = "";
  for (auto c : g.second)
    st += (c ? "1" : "0");
  return st;
}

string solve(int a, int b, int c, int d) {
  assert(a >= b);
  //	cout<<a<<" "<<b<<" "<<c<<" "<<d<<endl;
  string ans = "";
  // assert(a<=1010 && b<=1010);
  if (a == b) {
    for (int i = c; i < d; i++) {
      if (i % 2)
        ans += "1";
      else
        ans += "0";
    }
    return ans;
  }

  if (a == b + 1) {
    for (int i = c; i < d; i++) {
      if (i % 2)
        ans += "1";
      else
        ans += "0";
    }
    return ans;
  }

  int x = (a / (b + 1) + !!(a % (b + 1)));

  //	int aa=(b+1)*(a/(b+1)+!!(a%(b+1)));

  // cout<<x<<" "<<aa<<endl;

  if (a >= x * b) {
    for (int i = c; i < d; i++) {
      if (i % (x + 1) == x)
        ans += "1";
      else
        ans += "0";
    }
    return ans;
  }
  /*
  int nokori=x*b-a;
  string tani="";
  for(int i=0;i<x;i++)tani+="0";
  tani+="1";
  string s="";
  for(int i=0;i<b;i++)s+=tani;

  vector<int> ve;
  assert(s.length()==b*(x+1));
  ve.resize((int)s.length(),0);
  for(int i=0;i<b*(x+1);i++){
          if(s[i]=='1')ve[i]=1;
  }
  int cnt=1;
  for(int ima=b*(x);ima>=0;ima-=x+1){
          if(cnt%x==0)ve[ima]=1;
          cnt++;
  }
  for(int i=b*(x+1)-1;;i--)if(ve[i]==0){
          ve[i]=-1;
          nokori--;
          if(nokori==0) break;
  }
  cnt=0;
  for(int i=0;;i++)if(ve[i]>=0){
          if(c<=cnt && cnt<d){
                  ans+=s[i];
                  if(cnt==d-1)break;
          }
                  cnt++;

  }
  */
  // cout<<a<<" "<<b<<" "<<c<<" "<<d<<endl;
  swap(c, d);
  c = a + b - c;
  d = a + b - d;
  //	cout<<c<<" "<<d<<endl;
  int nokori = x * b - a;
  //	cout<<nokori<<endl;
  int d1 = nokori / (x * x - 1);
  // di 1--(x)個--10
  // (x+1)*d1文字
  //	cout<<"d1 "<<d1<<endl;
  nokori %= x * x - 1;
  int d2 = nokori / x;
  // d2は長さ 1----1
  // d2文字
  //	cout<<"d2 "<<d2<<endl;
  nokori %= x;

  int d3 = x - nokori;
  //	cout<<"d3 "<<d3<<endl;

  // 10-(d3)-0
  // d3+1文字

  for (int i = c; i < d; i++) {
    if ((x + 1) * d1 > i) {
      int ii = i % (x + 1);
      if (ii == x)
        ans += "0";
      else
        ans += "1";
    } else if ((x + 1) * d1 + d2 > i) {
      ans += "1";
    } else if ((x + 1) * d1 + d2 + d3 + 1 > i) {
      if (i == (x + 1) * d1 + d2)
        ans += "1";
      else
        ans += "0";
    } else {
      int ii = i - ((x + 1) * d1 + d2 + d3 + 1);
      ii %= x + 1;
      if (ii == 0)
        ans += "1";
      else
        ans += "0";
    }
  }

  // cout<<ans<<endl;

  reverse(ans.begin(), ans.end());
  return ans;
}

signed main() {

  cin.tie(0);
  ios::sync_with_stdio(false);
  //	cout<<solve_gu(8,10)<<endl;
  //	cout<<solve_gu(10,8)<<endl;
  //	return 0;
  //	cout<<solve(6,3,0,9)<<endl;
  //	for(int i=10;i<=60;i++)cout<<solve(i,10,0,10+i)<<endl;
  //	return 0;
  int q;
  cin >> q;
  for (int i = 0; i < q; i++) {
    int a, b, c, d;
    cin >> a >> b >> c >> d;
    c--;

    string s;
    if (a >= b) {
      s = solve(a, b, c, d);
      for (auto c : s) {
        if (c == '0')
          cout << 'A';
        else
          cout << 'B';
      }
    } else {
      s = solve(b, a, a + b - d, a + b - c);
      reverse(s.begin(), s.end());
      for (auto c : s) {
        if (c == '1')
          cout << 'A';
        else
          cout << 'B';
      }
    }

    cout << "\n";
  }
  return 0;
}