760. N-Queens with Fixed First-Queen Column (Count Solutions)

Classic N-Queens with a twist: Given two integers n and c, you must place n queens on an n x n chessboard such that no two queens attack each other (queens attack along rows, columns, and both diagonals). The constraint is that the queen in ROW 0 is FIXED at column c. Return the total number of distinct valid full placements.

Special cases:
- If n == 0, return 1 (the empty board has exactly one arrangement).
- If c < 0 or c >= n, return 0 (no valid placement).
Use recursive backtracking with row-by-row queen placement, starting from row 1.

Input: Two integers n and c separated by a comma.

Output: Return an integer — the number of valid placements.

Examples

Input: 4, 1
Output: 1
Explanation: On a 4x4 board with first queen at column 1, exactly one solution exists: (0,1),(1,3),(2,0),(3,2).

Input: 1, 0
Output: 1
Explanation: Single queen placed at (0,0). Trivially valid.

Input: 3, 0
Output: 0
Explanation: No 3-queens solutions exist (or with first queen at any column).

Constraints

• 0 <= n <= 13
• 0 <= c <= 14 (values >= n return 0)

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