You are provided with a collection of items, each having a unique weight. A buyer wishes to purchase a set of these items, subject to two strict conditions set by the market rules:

1. The total weight of the chosen items must be exactly equal to a target weight $W$.
2. The buyer must choose exactly $N$ items.

Given the available item weights, write a program to calculate the total number of distinct combinations (subsets) of exactly $N$ items that sum up to exactly $W$.

Input Format

• The first line consists of a single integer $W$, representing the target total weight.
• The second line contains two space-separated integers, $N$ and $X$, where $N$ is the exact number of items the buyer must select, and $X$ is the total number of items available.
• The third line contains $X$ space-separated integers representing the weights of the available items.

Output Format

• Print a single integer on a new line representing the total number of valid ways to choose exactly $N$ items that sum to $W$.

Constraints

• All $X$ weights are unique and given in strictly ascending order.
• $0 < W \le 500$
• $0 < N \le 50$
• $0 < X \le 100$

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Sample Input 1

20
3 10
1 2 4 5 10 11 13 15 17 19

Sample Output 1

4

Explanation 1: The target weight is $W = 20$, and the required number of items is $N = 3$. The 4 valid combinations of 3 items that sum to 20 are:

• 1, 2, 17
• 1, 4, 15
• 2, 5, 13
• 4, 5, 11

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Sample Input 2

45
7 19
1 2 4 5 6 8 9 10 12 13 15 16 17 18 19 20 21 23 24

Sample Output 2

12

Explanation 2: The target weight is $W = 45$, and the required number of items is $N = 7$. There are exactly 12 distinct subsets of 7 items from the given array that sum to 45 (e.g., {1, 2, 4, 5, 6, 8, 19}, {1, 2, 4, 5, 6, 9, 18}, etc.).