Sum of Prime Numbers#11661

Sum of Prime Numbers

1 second
256 megabytes
Medium

Given natural numbers and . Write a program that counts the number of ways (considering order) to represent the number as a sum of prime numbers.

Input

The first line contains a natural number (1 \leq A \leq 3000).

The second line contains a natural number (2 \leq N \leq 10).

Output

An integer – the answer to the problem or if no solution exists.

Examples

Example 1

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Note

In this example, the possible ways to represent the number as a sum of two prime numbers are:

10 = 3 + 7

10 = 5 + 5

10 = 7 + 3