Source

This problem is adapted from Long Long OJ. All rights reserved.

Description

Little A likes making flower baskets, so today he is going to pick some flowers.

Because Little A loves mathematics, the number of flowers he picks in each pile must be an odd prime number and the numbers should be in strictly increasing order. He picked $N$ piles of flowers, with a total of $M$ flowers. How many different possibilities are there for the number of flowers in each pile? Please list them separately.

Input

The input consists of a single line containing two integers $N$ and $M$, representing the number of piles of flowers picked by Little A and the total number of flowers, respectively.

Output

The output consists of several lines.

The first line contains an integer $K$, which represents the number of different possibilities for the number of flowers in each pile picked by Little A.

The following $K$ lines, each containing $N$ numbers, represent the number of flowers in each pile for the $i$-th possibility.

If $K=0$, output a single line with the string No Answer. (There is a dot at the end of No Answer.).

Samples

2 32

2
3 29
13 19

7 128

No Answer.

Tips

• $1 \leq N \leq 20$.
• $1 \leq M \leq 300$.