You are given four integers N, A, M, and B. You have N weights with a mass of A kg each, and M weights with a mass of B kg each.
Your task is to determine if all N+M weights can be partitioned into two piles such that both piles have the exact same total mass.
Input
The input consists of a single line containing four integers N, A, M, B (1 \le N, M \le 10^{11}, 1 \le A, B \le 10^7).
Output
Print "YES" if a valid partition exists, and "NO" otherwise.
Examples
| standard input | standard output |
|---|
| 2 1 1 2
| YES
|
| 1 1 1 2
| NO
|