As a final riddle, the mentor gives Fahim only three clues about a hidden set of N numbers — their sum, their product, and their maximum — and challenges him to reconstruct any set of numbers that fits. You are told: the sum of N positive integers is S, their product is Pr, and the maximum is M. Determine whether such a set of N positive integers can exist, and if so, output one valid example (any valid array). This is a constructive reasoning problem — think about the tightest possible bounds (e.g. what's the minimum possible sum given N-1 values of 1 and one value M?) before coding a search.
Input
Three integers N S Pr M on one line.
Output
"NO" if impossible, otherwise "YES" followed by N integers forming a valid example.
Constraints
1 ≤ N ≤ 20, 1 ≤ S, Pr, M ≤ 10^9
Sample Input
3 6 6 3
Sample Output
YES 1 2 3
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