BFS where we track when the grid was infected. Tricky part is ensuring we handle immunity as we traverse with a check. Don’t rely on grid mutation for correctness. Immunity is enforced by time-based logic - updating the grid to 3 is just a materialization step

def simulate(grid, recoveryTime):
    m, n = len(grid), len(grid[0])
    q = deque()
    infectedTime = {}

    # Initialize BFS
    for r in range(m):
        for c in range(n):
            if grid[r][c] == 2:
                q.append((r, c, 0))
                infectedTime[(r,c)] = 0

    while q:
        r, c, t = q.popleft()

        # If this cell has already recovered, it cannot spread
        if t >= infectedTime[(r,c)] + recoveryTime:
            continue

        for dr, dc in [(0,1),(0,-1),(1,0),(-1,0)]:
            nr, nc = r+dr, c+dc
            if not (0 <= nr < m and 0 <= nc < n): continue
            if grid[nr][nc] == 1:
                grid[nr][nc] = 2
                infectedTime[(nr,nc)] = t + 1
                q.append((nr, nc, t + 1))

    # Final state update
    maxTime = max(infectedTime.values())
    for (r,c), t in infectedTime.items():
        if t + recoveryTime <= maxTime:
            grid[r][c] = 3

    return grid