The Primes

In the square below, each row, each column and the two diagonals can be read as a five digit prime number. The rows are read from left to right. The columns are read from top to bottom. Both diagonals are read from left to right.

+---+---+---+---+---+
| 1 | 1 | 3 | 5 | 1 |
+---+---+---+---+---+
| 3 | 3 | 2 | 0 | 3 |
+---+---+---+---+---+
| 3 | 0 | 3 | 2 | 3 |
+---+---+---+---+---+
| 1 | 4 | 0 | 3 | 3 |
+---+---+---+---+---+
| 3 | 3 | 3 | 1 | 1 |
+---+---+---+---+---+ 

• The prime numbers' digits must sum to the same number.
• The digit in the top left-hand corner of the square is pre-determined (1 in the example).
• A prime number may be used more than once in the same square.
• If there are several solutions, all must be presented (sorted in numerical order as if the 25 digits were all one long number).
• A five digit prime number cannot begin with a zero (e.g., 00003 is NOT a five digit prime number).

PROGRAM NAME: prime3

INPUT FORMAT

A single line with two space-separated integers: the sum of the digits and the digit in the upper left hand corner of the square.

SAMPLE INPUT (file prime3.in)

11 1

OUTPUT FORMAT

Five lines of five characters each for each solution found, where each line in turn consists of a five digit prime number. Print a blank line between solutions. If there are no prime squares for the input data, output a single line containing "NONE".

SAMPLE OUTPUT (file prime3.out)

The above example has 3 solutions.

11351
14033
30323
53201
13313

11351
33203
30323
14033
33311

13313
13043
32303
50231
13331