Determine Legal Memory Access in a 2D Array

Consider a 2D array defined in C++ as (a[N][M]), where the memory is allocated in a continuous block. Traditionally, the valid indices are (a[0\ldots N-1][0\ldots M-1]). However, due to continuous memory allocation, accessing (a[p][q]) is translated to accessing the ((p \times M + q))-th element (0-indexed) from the beginning of the array. For example, if (a[2][3]) is defined, then (a[0][4]) will not access illegal memory because it refers to the 5th element starting at (a[0][0]), which corresponds to (a[1][1]).

Given the dimensions (N) and (M) of the array and an access attempt at (a[p][q]), determine whether this access will go outside the allocated memory. In other words, let (L = p \times M + q). If (L) is within the range ([0, N \times M - 1]) then the access is legal; otherwise, it is illegal.

Note: The input integers can be assumed to be such that the computation (p \times M + q) is done using standard integer arithmetic.

inputFormat

The input consists of a single line containing four integers (N), (M), (p), and (q) separated by spaces. (N) and (M) represent the dimensions of the array and (p), (q) represent the indices attempted in the access.

outputFormat

Output a single word: output NO if the memory access is legal (i.e. if (0 \leq p \times M + q < N \times M)); otherwise, output YES to indicate an illegal memory access.

sample

2 3 0 4

NO