Little T and Little J are playing a coin-flipping game with $$$n$$$ coins, all initially facing up. First, they agree on a number $$$k$$$. Little T then flips exactly $$$k$$$ coins to face down, but Little J does not know which ones.

After that, Little J must assign each coin to one of four operations:

1. Place in the first pile (no flip)
2. Place in the first pile and flip
3. Place in the second pile (no flip)
4. Place in the second pile and flip

Example: When $$$n=5$$$ with operation sequence 12341:

• Coins 1, 2, 5 $$$\to$$$ first pile (coin $$$2$$$ is flipped)
• Coins 3, 4 $$$\to$$$ second pile (coin $$$4$$$ is flipped)

The game is won by Little J if and only if both piles have the same number of coins facing up after all operations. One of the piles is allowed to contain zero coins.

Your task is to determine whether there exists an operation sequence that guarantees Little J's victory for any possible choice of $$$k$$$ flipped coins by Little T. If such a sequence exists, construct it; otherwise, output $$$-1$$$.