Path Sum Counter

Given a binary tree, find the number of paths that sum to a given value. A path is defined as any sequence of nodes in the tree where the sum of the node values equals the target sum. The input consists of the first line with the target sum (an integer), followed by the tree's node values in level order, where 'null' indicates absent nodes. The output should be a single integer representing the number of paths that sum to the target. Example Input: 22 5 4 8 11 null 13 4 7 2 null null null null 5 1 null null Example Output: 3