Problem: Vasya lagged behind at the University and got to the battlefield. Just joking! He's simply playing some computer game. The field is a flat platform with n trenches dug on it. The trenches are segments on a plane parallel to the coordinate axes. No two trenches intersect.

There is a huge enemy laser far away from Vasya. The laser charges for a seconds, and then shoots continuously for b seconds. Then, it charges for a seconds again. Then it shoots continuously for b seconds again and so on. Vasya knows numbers a and b. He also knows that while the laser is shooting, Vasya must be in the trench, but while the laser is charging, Vasya can safely move around the field. The main thing is to have time to hide in the trench before the shot. If Vasya reaches the trench exactly at the moment when the laser starts shooting, we believe that Vasya managed to hide. Coincidentally, the length of any trench in meters numerically does not exceed b.

Initially, Vasya is at point A. He needs to get to point B. Vasya moves at speed 1 meter per second in either direction. You can get in or out of the trench at any its point. Getting in or out of the trench takes no time. It is also possible to move in the trench, without leaving it.

What is the minimum time Vasya needs to get from point A to point B, if at the initial time the laser has just started charging? If Vasya cannot get from point A to point B, print -1. If Vasya reaches point B at the moment when the laser begins to shoot, it is believed that Vasya managed to reach point B.

Input

The first line contains two space-separated integers: a and b (1 ≤ a, b ≤ 1000), — the duration of charging and the duration of shooting, in seconds.

The second line contains four space-separated integers: Ax, Ay, Bx, By ( - 104 ≤ Ax, Ay, Bx, By ≤ 104) — the coordinates of points А and B. It is guaranteed that points A and B do not belong to any trench.

The third line contains a single integer: n (1 ≤ n ≤ 1000), — the number of trenches. 

Each of the following n lines contains four space-separated integers: x1, y1, x2, y2 ( - 104 ≤ xi, yi ≤ 104) — the coordinates of ends of the corresponding trench.

All coordinates are given in meters. It is guaranteed that for any trench either x1 = x2, or y1 = y2. No two trenches intersect. The length of any trench in meters doesn't exceed b numerically.

Output

If Vasya can get from point A to point B, print the minimum time he will need for it. Otherwise, print number -1.

The answer will be considered correct if the absolute or relative error does not exceed 10 - 4

Examples

Input

2 4
0 5 6 5
3
0 0 0 4
1 1 4 1
6 0 6 4


Output

19.0000000000


Input

5 10
0 0 10 10
1
5 0 5 9


Output

-1

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int OO = 1e9;
const long long INF = 1e18;
const int irand(int lo, int hi) {
  return ((double)rand() / (RAND_MAX + 1.0)) * (hi - lo + 1) + lo;
}
const long long lrand(long long lo, long long hi) {
  return ((double)rand() / (RAND_MAX + 1.0)) * (hi - lo + 1) + lo;
}
template <typename T>
T getnum() {
  int sign = 1;
  T ret = 0;
  char c;
  do {
    c = getchar();
  } while (c == ' ' || c == '\n');
  if (c == '-')
    sign = -1;
  else
    ret = c - '0';
  while (1) {
    c = getchar();
    if (c < '0' || c > '9') break;
    ret = 10 * ret + c - '0';
  }
  return sign * ret;
}
inline void ini(int &x) { x = getnum<int>(); }
inline void scani(int &x) { scanf("%d", &x); }
const double EPS = 1E-9;
const double PI = acos(-1.0);
const double INFD = 1E9;
double between_d(double x, double l, double r) {
  return (min(l, r) <= x + EPS && x <= max(l, r) + EPS);
}
double same_d(double x, double y) { return between_d(x, y, y); }
double dabs(double x) {
  if (x < EPS) return -x;
  return x;
}
struct point {
  double x, y;
  point() { x = y = 0.0; }
  point(double _x, double _y) {
    x = _x;
    y = _y;
  }
  bool operator<(point other) {
    if (x < other.x + EPS) return true;
    if (x + EPS > other.x) return false;
    return y < other.y + EPS;
  }
  bool operator==(point other) {
    return same_d(x, other.x) && same_d(y, other.y);
  }
};
double e_dist(point P1, point P2) { return hypot(P1.x - P2.x, P1.y - P2.y); }
double m_dist(point P1, point P2) {
  return dabs(P1.x - P2.x) + dabs(P1.y - P2.y);
}
double pointBetween(point P, point L, point R) {
  return (e_dist(L, P) + e_dist(P, R) == e_dist(L, R));
}
struct vec {
  double x, y;
  vec() { x = y = 0.0; }
  vec(double _x, double _y) {
    x = _x;
    y = _y;
  }
  vec(point A) {
    x = A.x;
    y = A.y;
  }
  vec(point A, point B) {
    x = B.x - A.x;
    y = B.y - A.y;
  }
};
vec scale(vec v, double s) { return vec(v.x * s, v.y * s); }
vec flip(vec v) { return vec(-v.x, -v.y); }
double dot(vec u, vec v) { return (u.x * v.x + u.y * v.y); }
double cross(vec u, vec v) { return (u.x * v.y - u.y * v.x); }
double norm_sq(vec v) { return (v.x * v.x + v.y * v.y); }
point translate(point P, vec v) { return point(P.x + v.x, P.y + v.y); }
point rotate(point P, point O, double angle) {
  vec v(O);
  P = translate(P, flip(v));
  return translate(point(P.x * cos(angle) - P.y * sin(angle),
                         P.x * sin(angle) + P.y * cos(angle)),
                   v);
}
point mid(point P, point Q) { return point((P.x + Q.x) / 2, (P.y + Q.y) / 2); }
double angle(point A, point O, point B) {
  vec OA(O, A), OB(O, B);
  return acos(dot(OA, OB) / sqrt(norm_sq(OA) * norm_sq(OB)));
}
int orientation(point P, point Q, point R) {
  vec PQ(P, Q), PR(P, R);
  double c = cross(PQ, PR);
  if (c < EPS) return -1;
  if (c > EPS) return 1;
  return 0;
}
struct line {
  double a, b, c;
  line() { a = b = c = 0.0; }
  line(double _a, double _b, double _c) {
    a = _a;
    b = _b;
    c = _c;
  }
  line(point P1, point P2) {
    if (P2 < P1) {
      point T;
      T = P1;
      P1 = P2;
      P2 = T;
    }
    if (same_d(P1.x, P2.x))
      a = 1.0, b = 0.0, c = -P1.x;
    else
      a = -(P1.y - P2.y) / (P1.x - P2.x), b = 1.0, c = -(a * P1.x) - P1.y;
  }
  line(point P, double slope) {
    if (same_d(slope, INFD))
      a = 1.0, b = 0.0, c = -P.x;
    else
      a = -slope, b = 1.0, c = -(a * P.x) - P.y;
  }
  bool operator==(line other) {
    return same_d(a, other.a) && same_d(b, other.b) && same_d(c, other.c);
  }
  double slope() {
    if (same_d(b, 0.0)) return INFD;
    return -(a / b);
  }
};
bool paralel(line L1, line L2) {
  return same_d(L1.a, L2.a) && same_d(L1.b, L2.b);
}
bool intersection(line L1, line L2, point &P) {
  if (paralel(L1, L2)) return false;
  P.x = (L2.b * L1.c - L1.b * L2.c) / (L2.a * L1.b - L1.a * L2.b);
  if (same_d(L1.b, 0.0))
    P.y = -(L2.a * P.x + L2.c);
  else
    P.y = -(L1.a * P.x + L1.c);
  return true;
}
double pointToLine(point P, point A, point B, point &C) {
  vec AP(A, P), AB(A, B);
  double u = dot(AP, AB) / norm_sq(AB);
  C = translate(A, scale(AB, u));
  return e_dist(P, C);
}
double lineToLine(line L1, line L2) {
  if (!paralel(L1, L2)) return 0.0;
  return dabs(L2.c - L1.c) / sqrt(L1.a * L1.a + L1.b * L1.b);
}
struct segment {
  point P, Q;
  line L;
  segment() {
    point T1;
    P = Q = T1;
    line T2;
    L = T2;
  }
  segment(point _P, point _Q) {
    if (_Q < _P) {
      point T1 = _P;
      _P = _Q;
      _Q = T1;
    }
    P = _P;
    Q = _Q;
    line T2(_P, _Q);
    L = T2;
  }
  bool operator==(segment other) { return P == other.P && Q == other.Q; }
};
bool onSegment(point P, segment second) {
  if (orientation(second.P, second.Q, P) != 0) return false;
  return between_d(P.x, second.P.x, second.Q.x) &&
         between_d(P.y, second.P.y, second.Q.y);
}
bool s_intersection(segment S1, segment S2) {
  double o1 = orientation(S1.P, S1.Q, S2.P);
  double o2 = orientation(S1.P, S1.Q, S2.Q);
  double o3 = orientation(S2.P, S2.Q, S1.P);
  double o4 = orientation(S2.P, S2.Q, S1.Q);
  if (o1 != o2 && o3 != o4) return true;
  if (o1 == 0 && onSegment(S2.P, S1)) return true;
  if (o2 == 0 && onSegment(S2.Q, S1)) return true;
  if (o3 == 0 && onSegment(S1.P, S2)) return true;
  if (o4 == 0 && onSegment(S2.Q, S2)) return true;
  return false;
}
double pointToSegment(point P, point A, point B, point &C) {
  vec AP(A, P), AB(A, B);
  double u = dot(AP, AB) / norm_sq(AB);
  if (u < EPS) {
    C = A;
    return e_dist(P, A);
  }
  if (u + EPS > 1.0) {
    C = B;
    return e_dist(P, B);
  }
  return pointToLine(P, A, B, C);
}
double segmentToSegment(segment S1, segment S2) {
  if (s_intersection(S1, S2)) return 0.0;
  double ret = INFD;
  point dummy;
  ret = min(ret, pointToSegment(S1.P, S2.P, S2.Q, dummy));
  ret = min(ret, pointToSegment(S1.Q, S2.P, S2.Q, dummy));
  ret = min(ret, pointToSegment(S2.P, S1.P, S1.Q, dummy));
  ret = min(ret, pointToSegment(S2.Q, S1.P, S1.Q, dummy));
  return ret;
}
const int N = 1005;
int a, b;
int n;
point start, endd;
segment sg[N];
queue<int> q;
int dist[N];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> a >> b;
  cin >> start.x >> start.y >> endd.x >> endd.y;
  cin >> n;
  for (int i = 1; i <= n; i += 1) {
    int a, b, c, d;
    cin >> a >> b >> c >> d;
    sg[i] = segment(point(a, b), point(c, d));
  }
  if (e_dist(start, endd) <= a) {
    cout << fixed << setprecision(12) << e_dist(start, endd) << endl;
    return 0;
  }
  double ans = OO;
  q.push(0);
  while (!q.empty()) {
    int now = q.front();
    q.pop();
    if (now == 0) {
      for (int i = 1; i <= n; i += 1) {
        point tmp;
        if (pointToSegment(start, sg[i].P, sg[i].Q, tmp) <= a) {
          if (dist[i] > 0) continue;
          dist[i] = a + b;
          q.push(i);
        }
      }
    } else {
      point tmp;
      if (pointToSegment(endd, sg[now].P, sg[now].Q, tmp) <= a) {
        ans = min(ans,
                  dist[now] + pointToSegment(endd, sg[now].P, sg[now].Q, tmp));
      }
      for (int i = 1; i <= n; i += 1) {
        if (segmentToSegment(sg[now], sg[i]) <= a) {
          if (dist[i] > 0) continue;
          dist[i] = dist[now] + a + b;
          q.push(i);
        }
      }
    }
  }
  if (ans == OO)
    cout << "-1" << endl;
  else
    cout << fixed << setprecision(12) << ans << endl;
  return 0;
}