Number Partition

You want to divide all integers from $1$ to $n$ into three piles, so that each integer belongs to exactly one pile.

Determine whether it is possible to make the sums of the three piles equal to $a,b,c$ in this order. If it is possible, output one such partition.

The order of the piles matters. The sum of the first pile must be $a$, the sum of the second pile must be $b$, and the sum of the third pile must be $c$.

The input is given in the following format.

$n$ $a\ b\ c$

If it is possible, print $\text{YES}$ on the first line.

Then print information about the three piles in the next $3$ lines. On the $i$-th of these lines, first print the number $k_i$ of integers in the $i$-th pile, followed by the integers in that pile separated by spaces.

The printed integers must contain every integer from $1$ to $n$ exactly once. The sums of the first, second, and third piles must be $a,b,c$, respectively.

If it is impossible, print $\text{NO}$ on the first line.

• $3 \leq n \leq 200\ 000$.
• $1 \leq a,b,c$.
• $a+b+c=\dfrac{n(n+1)}{2}$.