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E. Sum and product
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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