Harry Potter's birthday is coming soon! Hermione wants to prepare an unusual gift for him. She wants to give Harry a set of n magic candies. Each candy is characterized by its taste — an integer t
i . The pleasure that Harry will get from a set of sweets — is the sum of the flavors of all the candies in that set. Note that the flavors of the candies, like Harry's pleasure, do not have to be positive.
Hermione has a huge box of sweets that contains exactly one candy flavor t for every integer t from - 10
9 to 10
9. Hermione wants to take n chocolates from this box to make Harry's set.
Hermione wants Harry to enjoy the set of sweets given to him, exactly equal to the integer s . Help her choose the right set, or determine that it's not possible.
Input
The first line of the input contains a single integer n ( 1 ≤ n ≤ 100 ) — how many sweets Hermione wants to put in the set. The second line of the input contains a single integer s ( - 10
9 ≤ s ≤ 10
9 ) — the pleasure Harry must get from the set.
Imprint
If it is impossible to make the desired set of candies from Hermione's, print « NO ". Otherwise, in the first line print « YES », and in the second line randomly n numbers — candy flavors in the desired set. If there are several correct answers, print any of them.
Examples
| # |
Input |
Output |
| 1 |
3
10 |
YES
500000000 -500000000 10 |