Point on Rectangle Boundary

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

An axis-aligned rectangle has corners (0,0), (W,0), (W,H), and (0,H), with positive W and H. Determine whether integer point (x,y) lies on one of its four closed edges; a point outside an edge segment is not on the boundary.

Input

One line contains four integer values W,H,x,y.

Output

Print YES if the point is on a rectangle edge and NO otherwise.

Subtasks

• Subtask 1 (20 points): 1 <= W,H <= 100, and the point is guaranteed inside/on the rectangle.

• Subtask 2 (30 points): 1 <= W,H <= 10^6 and -10^6 <= x,y <= 2*10^6.

• Subtask 3 (50 points): 1 <= W,H <= 10^9 and -10^9 <= x,y <= 2*10^9.

Examples

Example 1

Input

5 3 5 2

Output

YES

Explanation

For this input, the case-specific computation and the required exact output are shown above. The point (5,2) is inside the closed rectangle and its x coordinate equals W, so it lies on the right edge.

Example 2

Input

5 3 5 4

Output

NO

Explanation

For this input, the case-specific computation and the required exact output are shown above. The point (5,4) is outside the rectangle because 4 exceeds H=3, despite x being W.