You are given integers N and D. Find N positive integers x1...xN such that the difference of their product and their sum equals D.

Input

The only line of input contains integers N (2 ≤ N ≤ 1000) and D (0 ≤ D ≤ 1000).

Output

Output N integers that satisfy the given condition in non-decreasing order (in a single line, separated with spaces). Note that some numbers can be equal. Numbers printed by you must not exceed 106.

Examples

Input

2 1


Output

2 3


Input

3 5


Output

1 2 8

Source: codeforces | Difficulty: MEDIUM_HARD


Solutions: