2018 IMO Shortlist C4

An anti-Pascal pyramid is a finite set of numbers, placed in a triangle-shaped array so that the first row of the array contains one number, the second row contains two numbers, the third row contains three numbers and so on; and, except for the numbers in the bottom row, each number equals the absolute value of the difference of the two numbers below it. For instance, the triangle below is an anti-Pascal pyramid with four rows, in which every integer from 1 to $1+2+3+4=10$ occurs exactly once: $$\begin{array}{cccc} & & 4 \\ & 2 & 6 & \\ & 5 \quad 7 \quad 1 \\ 8 & 3 & 10 & 9 . \end{array}$$ Is it possible to form an anti-Pascal pyramid with 2018 rows, using every integer from 1 to $1+2+\cdots+2018$ exactly once? (Iran)

反帕斯卡金字塔是一组有限的数字，放置在三角形数组中，使得数组的第一行包含一个数字，第二行包含两个数字，第三行包含三个数字，依此类推；并且，除了底行中的数字之外，每个数字都等于其下面的两个数字之差的绝对值。例如，下面的三角形是一个有四行的反帕斯卡金字塔，其中从 1 到 $1+2+3+4=10$ 的每个整数都只出现一次： $$\begin{array}{cccc} & & 4 \\ & 2 & 6 & \\ & 5 \quad 7 \quad 1 \\ 8 & 3 & 10 & 9 。 \end{array}$$ 是否可以使用从 1 到 $1+2+\cdots+2018$ 的每个整数一次形成一个具有 2018 行的反帕斯卡金字塔？ (伊朗)