Problem: It's a beautiful April day and Wallace is playing football with his friends. But his friends do not know that Wallace actually stayed home with Gromit and sent them his robotic self instead. Robo-Wallace has several advantages over the other guys. For example, he can hit the ball directly to the specified point. And yet, the notion of a giveaway is foreign to him. The combination of these features makes the Robo-Wallace the perfect footballer — as soon as the ball gets to him, he can just aim and hit the goal. He followed this tactics in the first half of the match, but he hit the goal rarely. The opposing team has a very good goalkeeper who catches most of the balls that fly directly into the goal. But Robo-Wallace is a quick thinker, he realized that he can cheat the goalkeeper. After all, they are playing in a football box with solid walls. Robo-Wallace can kick the ball to the other side, then the goalkeeper will not try to catch the ball. Then, if the ball bounces off the wall and flies into the goal, the goal will at last be scored.

Your task is to help Robo-Wallace to detect a spot on the wall of the football box, to which the robot should kick the ball, so that the ball bounces once and only once off this wall and goes straight to the goal. In the first half of the match Robo-Wallace got a ball in the head and was severely hit. As a result, some of the schemes have been damaged. Because of the damage, Robo-Wallace can only aim to his right wall (Robo-Wallace is standing with his face to the opposing team's goal).

The football box is rectangular. Let's introduce a two-dimensional coordinate system so that point (0, 0) lies in the lower left corner of the field, if you look at the box above. Robo-Wallace is playing for the team, whose goal is to the right. It is an improvised football field, so the gate of Robo-Wallace's rivals may be not in the middle of the left wall.

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In the given coordinate system you are given: 

  * y1, y2 — the y-coordinates of the side pillars of the goalposts of robo-Wallace's opponents; 
  * yw — the y-coordinate of the wall to which Robo-Wallace is aiming; 
  * xb, yb — the coordinates of the ball's position when it is hit; 
  * r — the radius of the ball. 



A goal is scored when the center of the ball crosses the OY axis in the given coordinate system between (0, y1) and (0, y2). The ball moves along a straight line. The ball's hit on the wall is perfectly elastic (the ball does not shrink from the hit), the angle of incidence equals the angle of reflection. If the ball bounces off the wall not to the goal, that is, if it hits the other wall or the goal post, then the opposing team catches the ball and Robo-Wallace starts looking for miscalculation and gets dysfunctional. Such an outcome, if possible, should be avoided. We assume that the ball touches an object, if the distance from the center of the ball to the object is no greater than the ball radius r.

Input

The first and the single line contains integers y1, y2, yw, xb, yb, r (1 ≤ y1, y2, yw, xb, yb ≤ 106; y1 < y2 < yw; yb + r < yw; 2·r < y2 - y1).

It is guaranteed that the ball is positioned correctly in the field, doesn't cross any wall, doesn't touch the wall that Robo-Wallace is aiming at. The goal posts can't be located in the field corners.

Output

If Robo-Wallace can't score a goal in the described manner, print "-1" (without the quotes). Otherwise, print a single number xw — the abscissa of his point of aiming. 

If there are multiple points of aiming, print the abscissa of any of them. When checking the correctness of the answer, all comparisons are made with the permissible absolute error, equal to 10 - 8. 

It is recommended to print as many characters after the decimal point as possible.

Examples

Input

4 10 13 10 3 1


Output

4.3750000000


Input

1 4 6 2 2 1


Output

-1


Input

3 10 15 17 9 2


Output

11.3333333333

Note

Note that in the first and third samples other correct values of abscissa xw are also possible.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class cf249a {
  public static void main(String[] args) {
    FastIO in = new FastIO(), out = in;
    double y1 = in.nextDouble();
    double y2 = in.nextDouble();
    double yw = in.nextDouble();
    double xb = in.nextDouble();
    double yb = in.nextDouble();
    double r = in.nextDouble();  
    yw -= r;
    double yt = y1+r;
    yt = 2*yw - yt;
    double dy1 = yt - yb;
    double dy2 = yw - yb;  
    double dx1 = xb;
    double dx2 = dy2*dx1/dy1;
    dx2 = xb - dx2;
    vec2 v1 = new vec2(dx2,yw);
    vec2 v2 = new vec2(0,y1+r);
    vec2 v3 = new vec2(0,y2);
    double dist = new line2(v1,v2).dist(v3);
    if(dist-1e-9 < r) 
      out.println(-1);
    else
      out.printf("%.10f%n", dx2);
    out.close();
  }
  static class GEOM {
    static double eps = 1e-9;
    static boolean eq(double x, double y) {
      return Math.abs(x-y) < eps;
    }
  }
  static class vec2 {
    double x,y;
    vec2(double a, double b) {x=a;y=b;}
    boolean eq(vec2 rhs) {return GEOM.eq(x,rhs.x) && GEOM.eq(y,rhs.y);}
    vec2 add(vec2 rhs) {return new vec2(x+rhs.x,y+rhs.y);}
    vec2 sub(vec2 rhs) {return new vec2(x-rhs.x,y-rhs.y);}
    vec2 scale(double s) {return new vec2(x*s,y*s);}
    vec2 midpoint(vec2 rhs) {return new vec2(.5*(x+rhs.x),.5*(y+rhs.y));}
    double dot(vec2 rhs) {return x*rhs.x+y*rhs.y;}
    double cross(vec2 rhs) {return x*rhs.y-y*rhs.x;}//pos->left,neg->right
    double mag() {return Math.sqrt(x*x+y*y);}
    double mag2() {return x*x+y*y;}
    double dist(vec2 rhs) {return sub(rhs).mag();}
    double dist2(vec2 rhs) {return sub(rhs).mag2();}
    vec2 normalize() {return scale(1./mag());} //assumes mag()!=0
    double angleBtwn(vec2 rhs) {return Math.atan2(cross(rhs),dot(rhs));}
    double angle() {return Math.atan2(y,x);}
    vec2 orthoCW() {return new vec2(y,-x);}
    vec2 orthoCCW() {return new vec2(-y,x);}
    vec2 reflect(vec2 n) {return sub(scale(-2*dot(n)));}//n==surface normal
    //[cos(t)  -sin(t)][x] = [x*cos(t)-y*sin(t)   x*sin(t)+y*cos(t)]
    //[sin(t)   cos(t)][y]
    vec2 rotate(double ang) {
      double nx = x*Math.cos(ang) - y*Math.sin(ang);
      double ny = x*Math.sin(ang) + y*Math.cos(ang);
      return new vec2(nx,ny);
    }
  }

  static class line2 {
    vec2 e1,e2;
    line2(vec2 a, vec2 b) {e1=a;e2=b;}
    vec2 getVec2() {return e2.sub(e1);}
    vec2 intersect(line2 rhs) {
      vec2 v1 = getVec2(), v2 = rhs.getVec2(), v3 = rhs.e1.sub(e1);
      double div = v1.cross(v2), sn = v3.cross(v2);
      double s = sn/div;
      if(Math.abs(div) < 1e-9) return null; //parallel lines
      vec2 p = v1.scale(s).add(e1);
      //segment intersection
      double r = rhs.scaleProj(p);
      if(s < 0 || r < 0 || s > 1 || r > 1) return null; 
      return p;
    }
    double scaleProj(vec2 p) {// 0.0 -> 1.0
      vec2 v1 = getVec2(); return v1.dot(p.sub(e1))/v1.mag2();
    }
    vec2 proj(vec2 p) {
      vec2 v1 = getVec2();
      double k = v1.dot(p.sub(e1))/v1.mag2();
      return v1.scale(k).add(e1);
    }
    boolean isLower(vec2 a, vec2 b, vec2 p) {
      return b.sub(a).dot(p.sub(a)) < 0;
    }
    boolean checkSides(vec2 a, vec2 b, vec2 c, vec2 d) {
      vec2 v1 = b.sub(a);
      return v1.cross(c.sub(a)) * v1.cross(d.sub(a)) <= 0;
    }
    boolean intersects(line2 rhs) { //checks for segment intersection
      vec2[][] v = {{e1,e2},{rhs.e1,rhs.e2}};
      for(int i=0; i<2; i++) for(int j=0; j<2; j++) 
        if(isLower(v[i][j],v[i][1-j],v[1-i][0]) && 
           isLower(v[i][j],v[i][1-j],v[1-i][1])) return false;
      return checkSides(e1,e2,rhs.e1,rhs.e2)&&checkSides(rhs.e1,rhs.e2,e1,e2);
    }
    double dist(vec2 p) {
      vec2 A = getVec2();
      double t = A.dot(p.sub(e1))/A.mag2();
      if(t>=1) return e2.dist(p);
      if(t<=0) return e1.dist(p);
      return p.dist(A.scale(t).add(e1));
    }
    double dist(line2 rhs) {
      if(intersects(rhs)) return 0.;
      return Collections.min(Arrays.asList(dist(rhs.e1),dist(rhs.e2),rhs.dist(e1),rhs.dist(e2)));
    }
  }

  static class FastIO extends PrintWriter {
    BufferedReader br;
    StringTokenizer st;

    public FastIO() {
      this(System.in, System.out);
    }

    public FastIO(InputStream in, OutputStream out) {
      super(new BufferedWriter(new OutputStreamWriter(out)));
      br = new BufferedReader(new InputStreamReader(in));
      scanLine();
    }

    public void scanLine() {
      try {
        st = new StringTokenizer(br.readLine().trim());
      } catch (Exception e) {
        throw new RuntimeException(e.getMessage());
      }
    }

    public int numTokens() {
      if (!st.hasMoreTokens()) {
        scanLine();
        return numTokens();
      }
      return st.countTokens();
    }

    public String next() {
      if (!st.hasMoreTokens()) {
        scanLine();
        return next();
      }
      return st.nextToken();
    }

    public double nextDouble() {
      return Double.parseDouble(next());
    }

    public long nextLong() {
      return Long.parseLong(next());
    }

    public int nextInt() {
      return Integer.parseInt(next());
    }
  }
}