#include <bits/stdc++.h>
using namespace std;
typedef priority_queue<pair<long long, pair<long long, long long>>,
                       vector<pair<long long, pair<long long, long long>>>,
                       greater<pair<long long, pair<long long, long long>>>>
    plpllgreaterq;
template <class o, class p, class q>
using tuple3q = priority_queue<tuple<o, p, q>, vector<tuple<o, p, q>>,
                               greater<tuple<o, p, q>>>;
template <class o, class p, class q, class r>
using tuple4q = priority_queue<tuple<o, p, q, r>, vector<tuple<o, p, q, r>>,
                               greater<tuple<o, p, q, r>>>;
template <class o, class p, class q, class r, class s>
using tuple5q =
    priority_queue<tuple<o, p, q, r, s>, vector<tuple<o, p, q, r, s>>,
                   greater<tuple<o, p, q, r, s>>>;
int dx[] = {-1, 0, 1, 0};
int dy[] = {0, -1, 0, 1};
const long long INF = 1000000007;
const int MAX = 2000010;
const int MOD = 1000000007;
long long fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++) {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}
long long COM(int n, int k) {
  if (n < k) return 0;
  if (n < 0 || k < 0) return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
long long getpow(long long b, long long x, long long md) {
  long long t = b;
  long long res = 1;
  while (x > 0) {
    if (x & 1) {
      res *= t;
      res %= md;
    }
    x >>= 1;
    t *= t;
    t %= md;
  }
  return res;
}
long long getpow(long long b, long long x) { return getpow(b, x, INF); }
long long modinv(long long x) { return getpow(x, INF - 2); }
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
class mint {
  int md = 1000000007;

 public:
  long long x;
  mint(long long x, long long md) {
    this->md = md;
    this->x = (x % md + md) % md;
  }
  mint(long long x = 0) : x((x % md + md) % md) {}
  mint operator-() const { return mint(-x); }
  mint& operator+=(const mint& a) {
    if ((x += a.x) >= md) x -= md;
    return *this;
  }
  mint& operator-=(const mint& a) {
    if ((x += md - a.x) >= md) x -= md;
    return *this;
  }
  mint& operator*=(const mint& a) {
    (x *= a.x) %= md;
    return *this;
  }
  mint operator+(const mint& a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint& a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint& a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(long long t) const {
    if (!t) return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1) a *= *this;
    return a;
  }
  mint inv() const { return pow(md - 2); }
  mint& operator/=(const mint& a) { return (*this) *= a.inv(); }
  mint operator/(const mint& a) const {
    mint res(*this);
    return res /= a;
  }
  friend ostream& operator<<(ostream& os, const mint& m) {
    os << m.x;
    return os;
  }
};
int pr[100010];
int lank[100010];
void uini(int n) {
  for (size_t i = 0; i <= n; i++) {
    pr[i] = i;
    lank[i] = 1;
  }
}
int parent(int x) {
  if (x == pr[x]) return x;
  return pr[x] = parent(pr[x]);
}
int same(int x, int y) { return parent(x) == parent(y); }
bool unit(int x, int y) {
  int px = parent(x);
  int py = parent(y);
  if (px == py) return false;
  if (lank[py] < lank[px]) {
    pr[py] = px;
    lank[px] += lank[py];
  } else {
    pr[px] = py;
    lank[py] += lank[px];
  }
  return true;
}
long long n, m;
int ci = 0;
struct Node {
  int key;
  int priority;
  Node *parent, *left, *right;
  Node(int key, int priority);
  Node() {}
};
Node NIL;
Node::Node(int key, int priority) : key(key), priority(priority) {
  left = &NIL;
  right = &NIL;
}
Node* root = new Node();
void cenrec(Node* k) {
  if (k->key == NIL.key) return;
  cenrec(k->left);
  cout << " " << k->key;
  cenrec(k->right);
}
void fastrec(Node* k) {
  if (k->key == NIL.key) return;
  cout << " " << k->key;
  fastrec(k->left);
  fastrec(k->right);
}
void insert(Node* v) {
  Node* y = &NIL;
  Node* x = root;
  while (x->key != NIL.key) {
    y = x;
    if (v->key < x->key) {
      x = x->left;
    } else {
      x = x->right;
    }
  }
  v->parent = y;
  if (y->key == NIL.key) {
    root = v;
  } else if (v->key < y->key) {
    y->left = v;
  } else {
    y->right = v;
  }
}
Node* find(Node* k, long long v) {
  if (k->key == NIL.key) return &NIL;
  if (k->key == v) return k;
  if (v < k->key) return find(k->left, v);
  return find(k->right, v);
}
void delp12(Node* x) {
  if (x->key == NIL.key) return;
  Node* l = x->left;
  Node* r = x->right;
  Node* pr = x->parent;
  if (l->key == NIL.key && r->key == NIL.key) {
    if (pr->left == x) {
      pr->left = &NIL;
    } else
      pr->right = &NIL;
  } else if (l->key != NIL.key) {
    if (pr->left == x) {
      pr->left = l;
    } else
      pr->right = l;
    l->parent = pr;
  } else if (r->key != NIL.key) {
    if (pr->left == x) {
      pr->left = r;
    } else
      pr->right = r;
    r->parent = pr;
  }
}
Node* get_next(Node* k) {
  if (k->key == NIL.key) return &NIL;
  Node* res = get_next(k->left);
  if (res->key != NIL.key) return res;
  return k;
}
void del(Node* x) {
  if (x->key == NIL.key) return;
  Node* l = x->left;
  Node* r = x->right;
  Node* pr = x->parent;
  if (l->key != NIL.key && r->key != NIL.key) {
    Node* nex = get_next(r);
    x->key = nex->key;
    delp12(nex);
  } else {
    delp12(x);
  }
}
Node* rightRotate(Node* t) {
  Node* s = t->left;
  t->left = s->right;
  s->right = t;
  return s;
}
Node* leftRotate(Node* t) {
  Node* s = t->right;
  t->right = s->left;
  s->left = t;
  return s;
}
Node* _insert(Node* t, int key, int priority) {
  if (t->key == NIL.key) {
    return new Node(key, priority);
  }
  if (key == t->key) {
    return t;
  }
  if (key < t->key) {
    t->left = _insert(t->left, key, priority);
    if (t->priority < t->left->priority) {
      t = rightRotate(t);
    }
  } else {
    t->right = _insert(t->right, key, priority);
    if (t->priority < t->right->priority) {
      t = leftRotate(t);
    }
  }
  return t;
}
Node* delete1(Node* t, int key);
Node* _delete(Node* t, int key) {
  if (t->left->key == NIL.key && t->right->key == NIL.key) {
    return &NIL;
  } else if (t->left->key == NIL.key) {
    t = leftRotate(t);
  } else if (t->right->key == NIL.key) {
    t = rightRotate(t);
  } else {
    if (t->left->priority > t->right->priority) {
      t = rightRotate(t);
    } else
      t = leftRotate(t);
  }
  return delete1(t, key);
}
Node* delete1(Node* t, int key) {
  if (t->key == NIL.key) {
    return &NIL;
  }
  if (key < t->key) {
    t->left = delete1(t->left, key);
  } else if (key > t->key) {
    t->right = delete1(t->right, key);
  } else
    return _delete(t, key);
  return t;
}
int H;
int left(int i) { return i * 2 + 1; }
int right(int i) { return i * 2 + 2; }
class edge {
 public:
  int from, to, i;
  long long val;
  edge() {}
  edge(long long to) : to(to) {}
  edge(long long to, long long i) : to(to), i(i) {}
  edge(long long from, long long to, long long val)
      : from(from), to(to), val(val) {}
};
class LCA {
 private:
  vector<vector<edge>> v;
  vector<vector<int>> parent;
  vector<int> depth;
  void dfs(int n, int m, int d) {
    parent[0][n] = m;
    depth[n] = d;
    for (auto x : v[n]) {
      if (x.to != m) dfs(x.to, n, d + 1);
    }
  }

 public:
  LCA(long long N, long long root, vector<vector<edge>>& tree) {
    v = tree;
    parent = vector<vector<int>>(21, vector<int>(N + 1, 0));
    depth = vector<int>(N + 1, 0);
    dfs(root, -1, 0);
    for (int j = 0; j + 1 < 20; j++) {
      for (int i = 1; i <= N; i++) {
        if (parent[j][i] < 0)
          parent[j + 1][i] = -1;
        else
          parent[j + 1][i] = parent[j][parent[j][i]];
      }
    }
  }
  int lca(int n, int m) {
    if (depth[n] > depth[m]) swap(n, m);
    for (int j = 0; j < 20; j++) {
      if ((depth[m] - depth[n]) >> j & 1) m = parent[j][m];
    }
    if (n == m) return n;
    for (int j = 19; j >= 0; j--) {
      if (parent[j][n] != parent[j][m]) {
        n = parent[j][n];
        m = parent[j][m];
      }
    }
    return parent[0][n];
  }
  int dep(int n) { return depth[n]; }
};
long long k;
int _rank[1010];
int temp[1010];
bool compare_sa(int i, int j) {
  if (_rank[i] != _rank[j])
    return _rank[i] < _rank[j];
  else {
    int ri = i + k <= n ? _rank[i + k] : -1;
    int rj = j + k <= n ? _rank[j + k] : -1;
    return ri < rj;
  }
}
void construct_sa(string S, int* sa) {
  n = S.length();
  for (size_t i = 0; i <= n; i++) {
    sa[i] = i;
    _rank[i] = i < n ? S[i] : -1;
  }
  for (k = 1; k <= n; k *= 2) {
    sort(sa, sa + n + 1, compare_sa);
    temp[sa[0]] = 0;
    for (size_t i = 1; i <= n; i++) {
      temp[sa[i]] = temp[sa[i - 1]] + (compare_sa(sa[i - 1], sa[i]) ? 1 : 0);
    }
    for (size_t i = 0; i <= n; i++) {
      _rank[i] = temp[i];
    }
  }
}
bool contain(string S, int* sa, string T) {
  int a = 0, b = S.length();
  while (b - a > 1) {
    int c = (a + b) / 2;
    if (S.compare(sa[c], T.length(), T) < 0)
      a = c;
    else
      b = c;
  }
  return S.compare(sa[b], T.length(), T) == 0;
}
class BIT {
  static const int MAX_N = 500010;

 public:
  BIT() { memset(bit, 0, sizeof(bit)); }
  long long bit[MAX_N + 1], n;
  long long sum(int i) {
    long long s = 0;
    while (i > 0) {
      s += bit[i];
      i -= i & -i;
    }
    return s;
  }
  void add(int i, int x) {
    while (i <= n) {
      bit[i] += x;
      i += i & -i;
    }
  }
};
struct UnionFind {
  vector<int> A;
  UnionFind(int n) : A(n, -1) {}
  int find(int x) {
    if (A[x] < 0) return x;
    return A[x] = find(A[x]);
  }
  void unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return;
    if (A[x] > A[y]) swap(x, y);
    A[x] += A[y];
    A[y] = x;
  }
  int ngroups() {
    int ans = 0;
    for (auto a : A)
      if (a < 0) ans++;
    return ans;
  }
};
vector<long long> getp(long long n) {
  vector<long long> res;
  long long a = 2;
  if (n % 2 == 0) {
    res.push_back(2);
    while (n % 2 == 0) n /= 2;
  }
  for (long long i = 3; i * i <= n; i += 2) {
    if (n % i == 0) {
      res.push_back(i);
      while (n % i == 0) n /= i;
    }
  }
  if (n != 1) res.push_back(n);
  return res;
}
vector<long long> getp2(long long n) {
  vector<long long> res;
  long long a = 2;
  if (n % 2 == 0) {
    while (n % 2 == 0) {
      n /= 2;
      res.push_back(2);
    }
  }
  for (long long i = 3; i * i <= n; i += 2) {
    if (n % i == 0) {
      while (n % i == 0) {
        n /= i;
        res.push_back(i);
      }
    }
  }
  if (n != 1) res.push_back(n);
  return res;
}
vector<pair<long long, long long>> getp3(long long n) {
  vector<pair<long long, long long>> res;
  long long a = 2;
  int si = 0;
  if (n % 2 == 0) {
    res.push_back(make_pair(2, 0));
    while (n % 2 == 0) {
      n /= 2;
      res[si].second++;
    }
    si++;
  }
  for (long long i = 3; i * i <= n; i += 2) {
    if (n % i == 0) {
      res.push_back(make_pair(i, 0));
      while (n % i == 0) {
        n /= i;
        res[si].second++;
      }
      si++;
    }
  }
  if (n != 1) {
    res.push_back(make_pair(n, 1));
  }
  return res;
}
vector<long long> getDivisors(long long n) {
  vector<long long> res;
  long long a = 2;
  res.push_back(1);
  for (long long i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      res.push_back(i);
      if (n / i != i) res.push_back(n / i);
    }
  }
  return res;
}
struct ve {
 public:
  vector<ve> child;
  int _t = INF;
  ve(int t) : _t(t) {}
  ve(ve _left, ve _right) {
    _t = _left._t + _right._t;
    child.push_back(_left);
    child.push_back(_right);
  }
  bool operator<(const ve& t) const { return _t > t._t; }
};
vector<bool> elas(long long n) {
  vector<bool> r(n);
  fill(r.begin(), r.end(), 1);
  r[0] = 0;
  r[1] = 0;
  for (long long i = 2; i * i < n; i++) {
    if (!r[i]) continue;
    long long ti = i * 2;
    while (ti < n) {
      r[ti] = false;
      ti += i;
    }
  }
  return r;
}
bool isPrime(long long v) {
  for (long long i = 2; i * i <= v; i++) {
    if (v % i == 0) return false;
  }
  return true;
}
class SegTree {
 public:
  const static int MAX_N = 100010;
  const static int DAT_SIZE = (1 << 18) - 1;
  int N, Q;
  int A[MAX_N];
  long long data[DAT_SIZE], datb[DAT_SIZE];
  void init(int _n) {
    N = 1;
    while (N < _n) N <<= 1;
    memset(data, 0, sizeof(data));
    memset(datb, 0, sizeof(datb));
  }
  void init(int _n, long long iv) {
    N = 1;
    while (N < _n) N <<= 1;
    for (long long i = 0; i < DAT_SIZE; i++) {
      data[i] = iv;
      datb[i] = iv;
    }
  }
  void add(int a, int b, int x) { add(a, b + 1, x, 0, 0, N); }
  void add(int a, int b, int x, int k, int l, int r) {
    if (a <= l && r <= b) {
      data[k] += x;
    } else if (l < b && a < r) {
      datb[k] += (min(b, r) - max(a, l)) * x;
      add(a, b, x, k * 2 + 1, l, (l + r) / 2);
      add(a, b, x, k * 2 + 2, (l + r) / 2, r);
    }
  }
  void change(int a, int b, int x) { change(a, b + 1, x, 0, 0, N); }
  void change(int a, int b, int x, int k, int l, int r) {
    if (a <= l && r <= b) {
      data[k] = x;
    } else if (l < b && a < r) {
      datb[k] = x;
      change(a, b, x, k * 2 + 1, l, (l + r) / 2);
      change(a, b, x, k * 2 + 2, (l + r) / 2, r);
    }
  }
  long long sum(int a, int b) { return sum(a, b + 1, 0, 0, N); }
  long long sum(int a, int b, int k, int l, int r) {
    if (b <= l || r <= a) {
      return 0;
    }
    if (a <= l && r <= b) {
      return data[k] * (r - l) + datb[k];
    }
    long long res = (min(b, r) - max(a, l)) * data[k];
    res += sum(a, b, k * 2 + 1, l, (l + r) / 2);
    res += sum(a, b, k * 2 + 2, (l + r) / 2, r);
    return res;
  }
};
class Segment;
class Circle;
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(a * x, a * y); }
  Point operator/(double a) { return Point(x / a, y / a); }
  double abs() { 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) < (1e-10) && fabs(y - p.y) < (1e-10);
  }
  static double dot(Point a, Point b) { return a.x * b.x + a.y * b.y; }
  static double cross(Point a, Point b) { return a.x * b.y - a.y * b.x; }
  static bool isOrthogonal(Point a, Point b) {
    return (std::abs(dot(a, b) - 0.0) < (1e-10));
  }
  static bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
    return isOrthogonal(a1 - a2, b1 - b2);
  }
  static bool isOrthogonal(Segment s1, Segment s2);
  static bool isPalallel(Point a, Point b) {
    return (std::abs(cross(a, b) - 0.0) < (1e-10));
  }
  static bool isPalallel(Point a1, Point a2, Point b1, Point b2) {
    return isPalallel(a1 - a2, b1 - b2);
  }
  static bool isPalallel(Segment s1, Segment s2);
  static const int COUNTER_CLOCKWISE = 1;
  static const int CLOCKWISE = -1;
  static const int ONLINE_BACK = 2;
  static const int ONLINE_FRONT = -2;
  static const int ON_SEGMENT = 0;
  static int ccw(Point p0, Point p1, Point p2) {
    Point a = p1 - p0;
    Point b = p2 - p0;
    if (cross(a, b) > (1e-10)) return COUNTER_CLOCKWISE;
    if (cross(a, b) < -(1e-10)) return CLOCKWISE;
    if (dot(a, b) < -(1e-10)) return ONLINE_BACK;
    if (a.norm() < b.norm()) return ONLINE_FRONT;
    return ON_SEGMENT;
  }
  static bool intersect(Point p1, Point p2, Point p3, Point p4) {
    return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 &&
            ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
  }
  static bool intersect(Segment s1, Segment s2);
  static Point project(Segment s, Point p);
  static Point reflect(Segment s, Point p);
  static Point getDistance(Point a, Point b) { return (a - b).abs(); }
  static double getDistanceLP(Segment s, Point p);
  static double getDistanceSP(Segment s, Point p);
  static double getDistance(Segment s1, Segment s2);
  static Point getIntersection(Segment s1, Segment s2);
  static pair<Point, Point> crossPoints(Circle c, Segment s);
  static int contains(vector<Point> g, Point p) {
    int n = g.size();
    bool x = false;
    for (long long i = 0; i < n; i++) {
      Point a = g[i] - p, b = g[(i + 1) % n] - p;
      if (std::abs(cross(a, b)) < (1e-10) && dot(a, b) < (1e-10)) return 1;
      if (a.y > b.y) swap(a, b);
      if (a.y < (1e-10) && (1e-10) < b.y && cross(a, b) > (1e-10)) x = !x;
    }
    return x ? 2 : 0;
  }
  static vector<Point> andrewScan(vector<Point> s) {
    vector<Point> u, l;
    if (s.size() < 3) return s;
    sort(s.begin(), s.end());
    u.push_back(s[0]);
    u.push_back(s[1]);
    l.push_back(s[s.size() - 1]);
    l.push_back(s[s.size() - 2]);
    for (int i = 2; i < s.size(); i++) {
      for (int _n = u.size();
           _n >= 2 && ccw(u[_n - 2], u[_n - 1], s[i]) > CLOCKWISE; _n--) {
        u.pop_back();
      }
      u.push_back(s[i]);
    }
    for (int i = s.size() - 3; i >= 0; i--) {
      for (int _n = l.size();
           _n >= 2 && ccw(l[_n - 2], l[_n - 1], s[i]) > CLOCKWISE; _n--) {
        l.pop_back();
      }
      l.push_back(s[i]);
    }
    reverse(l.begin(), l.end());
    for (int i = u.size() - 2; i >= 1; i--) {
      l.push_back(u[i]);
    }
    return l;
  }
  void get_cin() { cin >> x >> y; }
};
class Segment {
 public:
  Point p1, p2;
  Segment() {}
  Segment(Point p1, Point p2) : p1(p1), p2(p2) {}
  void get_cin() { cin >> p1.x >> p1.y >> p2.x >> p2.y; }
  Point p1tp2() { return p2 - p1; }
  Point p2tp1() { return p1 - p2; }
  double abs() { return std::abs(norm()); }
  double norm() { return (p2 - p1).norm(); }
};
bool Point::isOrthogonal(Segment s1, Segment s2) {
  return (std::abs(dot(s1.p2 - s1.p1, s2.p2 - s2.p1) - 0.0) < (1e-10));
}
bool Point::isPalallel(Segment s1, Segment s2) {
  return (std::abs(cross(s1.p2 - s1.p1, s2.p2 - s2.p1) - 0.0) < (1e-10));
}
bool Point::intersect(Segment s1, Segment s2) {
  return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
Point Point::project(Segment s, Point p) {
  Point base = s.p2 - s.p1;
  double r = Point::dot(p - s.p1, base) / base.norm();
  return s.p1 + base * r;
}
Point Point::reflect(Segment s, Point p) { return (project(s, p) * 2) - p; }
double Point::getDistanceLP(Segment s, Point p) {
  return std::abs(cross(s.p2 - s.p1, p - s.p1) / (s.p2 - s.p1).abs());
}
double Point::getDistanceSP(Segment s, Point p) {
  if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return (p - s.p1).abs();
  if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return (p - s.p2).abs();
  return getDistanceLP(s, p);
}
double Point::getDistance(Segment s1, Segment s2) {
  if (intersect(s1, s2)) return 0.0;
  return min({getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2),
              getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)});
}
Point Point::getIntersection(Segment s1, Segment s2) {
  auto bs = s1.p2 - s1.p1;
  auto n1 = s2.p1 - s1.p1;
  auto n2 = s2.p2 - s1.p1;
  auto c1 = std::abs(cross(n1, bs)) / bs.norm();
  auto c2 = std::abs(cross(n2, bs)) / bs.norm();
  return s2.p1 + (s2.p2 - s2.p1) * (c1 / (c1 + c2));
}
double arg(Point p) { return atan2(p.y, p.x); }
Point polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }
class Circle {
 public:
  Point c;
  double r;
  Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}
  void get_cin() { cin >> c.x >> c.y >> r; }
  static pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
    double d = (c1.c - c2.c).abs();
    double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
    double t = arg(c2.c - c1.c);
    return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
  }
};
pair<Point, Point> Point::crossPoints(Circle c, Segment s) {
  auto pp = project(s, c.c);
  auto f = (pp - c.c).norm();
  auto mu = sqrt(c.r * c.r - f);
  auto e = s.p1tp2() / s.p1tp2().abs();
  return make_pair(pp + e * mu, pp - e * mu);
}
long long divRm(string s, long long x) {
  long long r = 0;
  for (long long i = 0; i < s.size(); i++) {
    r *= 10;
    r += s[i] - '0';
    r %= x;
  }
  return r;
}
long long cmbi(long long x, long long b) {
  long long res = 1;
  for (size_t i = 0; i < b; i++) {
    res *= x - i;
    res %= INF;
    res *= inv[b - i];
    res %= INF;
  }
  return res;
}
double digsum(long long x) {
  long long res = 0;
  while (x > 0) {
    res += x % 10;
    x /= 10;
  }
  return res;
}
bool check_parindrome(string s) {
  int n = s.size();
  for (long long i = 0; i < n / 2; i++) {
    if (s[i] != s[n - i - 1]) {
      return false;
    }
  }
  return true;
}
long long npr(long long n, long long r) {
  if (r == 0) return 1;
  return ((fac[n] * modinv(fac[n - r])) % INF);
}
vector<long long> zalgo(string s) {
  long long c = 0;
  vector<long long> a(s.size());
  long long si = s.size();
  for (long long i = 1; i < s.size(); i++) {
    if (i + a[i - c] < c + a[c]) {
      a[i] = a[i - c];
    } else {
      long long j = max(0LL, a[c] - (i - c));
      while (i + j < si && s[j] == s[i + j]) {
        j++;
      }
      a[i] = j;
      c = i;
    }
  }
  a[0] = s.size();
  return a;
}
string decStrNum(string s) {
  long long si = s.size();
  for (int i = si - 1; i >= 0; i--) {
    if (s[i] == '0') {
      s[i] = '9';
      continue;
    }
    s[i] = s[i] - 1;
    break;
  }
  return s;
}
void solv() {
  cin >> n;
  for (long long i = 0; i < n; i++) {
    long long a, b, c, d;
    cin >> a >> b >> c >> d;
    if (b > a || b > d) {
      cout << "No" << endl;
      continue;
    }
    if (c + 1 >= b) {
      cout << "Yes" << endl;
      continue;
    }
    long long gc = gcd(b, d);
    long long rm = a % b;
    long long inter = (b - rm);
    long long v = (inter / gc) * gc;
    if (c < v && v < b) {
      cout << "No" << endl;
      continue;
    }
    v -= gc;
    if (c < v && v < b) {
      cout << "No" << endl;
      continue;
    }
    cout << "Yes" << endl;
  }
}
int main() {
  COMinit();
  solv();
  return 0;
}
