Source

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

Problem 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 Format

One line consisting of two integers $N, M\ (1 \le N \le 20, 1 \le M \le 300)$.

Output Format

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.

For special cases, if $K = 0$, just ignore the format above and output a single line with the string No Answer..

Samples

2 32

2
3 29
13 19

7 128

No Answer.

Data Range

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