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E. Sum and product

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given integers *N* and *D*. Find *N* positive integers *x*_{1}...*x*_{N} 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 10^{6}.

Examples

Input

2 1

Output

2 3

Input

3 5

Output

1 2 8

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