Deciding to stock up on pens for the whole new school year, Igor calculated that he needed M pens.
His favorite online store has a handy — he can immediately add to the order a package of any number of pens from 1 to N. True, it turned out that it was impossible to add two packages of the same size to the order. For example, if Igor needs to buy M = 12 pens, and the maximum number of pens in a package is N = 10, then Igor can add a package of 7 pens and a package of 5 pens to the order, but he will not be able to add two packages of 6 pens.< br />
Place an order for M pens using the minimum number of different packages.
Input
The first line of the input contains the number N — maximum size of one package (1 ≤ N ≤ 10
9 ). The second line of the input contains an integer M — required number of pens per order (1 ≤ M ≤ 10
9 ).
Imprint
The program should output one or more numbers from 1 to N — the sizes of the selected packages in any order. There are several possible solutions, print any of them. If the solution does not exist, you must print a single number "0".
Examples
| # |
Input |
Output |
| 1 |
10
12 |
5
7 |
| 2 |
2
5 |
0 |